ASSIGNMENT 2
Q.1) Directions: For each of these questions, choose the option (a, b, C or d)
that is TRUE and give a justification on why you chose that answer.
1. If in a discrete series 85% values are less than 30, then it describes what value
a. 𝑃30 = 85
b. 𝑄1 = 30
c. 𝐷85 = 75
d. 𝑃85 = 30
2. If the coefficient of variation for prices is 5.483% and the mean price is Rs
15.5, then the variance price 𝑅𝑠 2 is equal to
a. 0.85
b. 84.9865
c. 28.269
d. 0.7225
3. Through visualization not mathematically determine the location of mean,
median and mode classes from the given Histogram of Prices of 300 cars.
a. 𝑀𝑒𝑎𝑛 = 1.449 − 1.995, 𝑚𝑒𝑑𝑖𝑎𝑛 = 1.995 − 2.495, 𝑚𝑜𝑑𝑒
2.495 − 2.995
b. 𝑀𝑒𝑎𝑛 = 1.449 − 1.995, 𝑚𝑒𝑑𝑖𝑎𝑛 = 2.495 − 2.995, 𝑚𝑜𝑑𝑒
1.995 − 2.495
c. 𝑀𝑒𝑎𝑛 = 2.995 − 3.495, 𝑚𝑒𝑑𝑖𝑎𝑛 = 2.495 − 2.995, 𝑚𝑜𝑑𝑒
1.995 − 2.495
d. 𝑀𝑒𝑎𝑛 = 1.995 − 2.495, 𝑚𝑒𝑑𝑖𝑎𝑛 = 1.995 − 2.495, 𝑚𝑜𝑑𝑒
1.995 − 2.495
=
=
=
=
4. The mean marks got by 68 students in the subject of Statistics are 65. The
mean of the top 10 of them was found to be 80 and the mean of the last 10
was known to be 50. The mean of the remaining 48 students is determined by
a. 60
b. 65
c. 0
d. 48
5.
Which of the following statement is not a property of the standard deviation?
a. It is always negative number
b. It is affected by extreme values in a data set
c. It is based on all the values in the data set
d. It is the most widely used measure of dispersion
6. The following data represent the numbers of minor penalties accrued by each
of the 30 National Hockey League franchises during the 2007–08 regular
season.
318
378
405
336
381
409
337
384
417
339
385
431
362
386
433
363
387
434
366
390
438
369
393
444
372
395
461
375
403
480
The 8th Decile penalties of League will be determined as
a. 431
b. 417
c. 433
431+433
d.
2
7. Geometric mean and harmonic mean for the values 3, -11, 0, 63, -14, 100 are
a. 0 and 3
b. 3 and -3
c. 0 and 0
d. Infinite and impossible
8. Which of the following is the mean of the squared deviations of x values from
the mean?
a. Mean deviation from mean
b. Variance
c. Standard error
d. Standard deviation
9. The mean of 20 values calculated as 312.6452. which of the following is
always true?
a. ∑(𝑋 − 312.6452) = 20
b. ∑(𝑋 − 312.6452) ≥ 20
c. ∑(𝑋 − 312.6452) = 0
d. ∑(𝑋 − 312.6452) ≤ 0
10. In a study of distances travelled to a college by commuting students, data
from 100 commuters yielded a mean of 8.73 miles. After the mean was
calculated, data came in late from three students, with respective distances of
11.5, 7.6, and 10.0 miles. Calculate the mean distance for all 103 students.
a. 8.73
b. 9.021
c. 37.83
d. 8.75
11. Refer to the graph below
Frequency Polygone
139
120
83
52
32
1
64
0
67
9
70
3
73
76
79
82
85
88
2
91
A. Mode weight is
a. 78.9
b. 82
c. 80.5
d. 80
B. Median weight is
a. 78.9
b. 82
c. 80.5
d. 80
C. Is this data skewed in any direction?
a. Yes, positively skewed
c. No, symmetrical
b. Yes, negatively skewed
d. Not symmetrical nor skewed
12. Consider the following two data sets.
Data Set I
12
25
37
8
41
Data Set II
19
32
44
15
48
Notice that each value of the second data set is obtained by adding 7 to the
corresponding value of the first data set. The mean and standard deviation for
Data Set I is 24.6 and 14.6389 respectively. Then the mean and variance for
Data Set II is equal to
a.
b.
c.
d.
Mean = 24.6 and Variance = 214.3
Mean = 31.6 and Variance = 14.6389
Mean = 31.6 and Variance = 214.3
Mean = 24.6 and Variance = 14.6389
13. If the coefficient of variation for prices is 5.483% and the variance price
𝑅𝑠 2 0.7225 then mean is equal to
a. 1.3177
b. 15.5
c. 7.5889
d. 0.5483
14. Through visualization not mathematically determine the location of mean,
median and mode classes from the given Histogram.
a. 𝑀𝑒𝑎𝑛 = 10.3, 𝑚𝑒𝑑𝑖𝑎𝑛 = 10.1, 𝑚𝑜𝑑𝑒 = 10.1
b. Mean = 10.01, median = 10.2, mode = 10.1
c. 𝑀𝑒𝑎𝑛 = 10.0, 𝑚𝑒𝑑𝑖𝑎𝑛 = 10.2, 𝑚𝑜𝑑𝑒 = 10.1
d. 𝑀𝑒𝑎𝑛 = 10.3, 𝑚𝑒𝑑𝑖𝑎𝑛 = 10.2, 𝑚𝑜𝑑𝑒 = 10.2
15. On a 300-mile auto trip, Lisa covered 52 mph for the first 100 miles, 65 mph
for the second 100 miles, and 58 mph for the last 100 miles. The average
speed covered by Lisa for the trip equals to
a. 59
b. 58.09
c. 58.33
d. 57.85
16. A small country bought oil from three different sources in one week, as
shown in the following table.
Source
Barrels Purchased.
Price per Barrel ($)
Mexico
1000
51
Kuwait
200
64
Spot Market
100
70
The mean price per barrel for all 1300 barrels of oil purchased in that week
equals to
a. 61.667
b. 433.33
c. 54.46
d. 64
17. Calculate The following data represent the numbers of minor penalties
accrued by each of the 40 National Hockey League franchises during the
2007–08 regular season.
1.6
3.3
4.4
1.9
3.4
4.5
2.2
3.4
4.7
2.5
3.4
4.7
2.6
3.5
2.6
3.5
2.9
3.6
3.0
3.7
3.0
3.7
3.1
3.7
3.1
3.8
3.1
3.8
3.1
3.9
3.2
3.9
3.2
4.1
The 9th Decile penalties of League will be determined as
a. 4.3
b. 4.4
4.3+4.4
c.
2
d.
4.2+4.3
2
3.2
4.1
3.3
4.2
3.3
4.3
18. If the three observations are a = 2, b = - 2 and c = 2 then their geometric mean
will be:
a. 2
b. 0
c. infinite
d. – 2
19. The following data give the numbers of times 10 persons used their credit
cards during the past 3 months. Mean deviation from mean is equal to
9
6
28
14
2
18
7
3
16
6
a. 0
b. 64.8
c. 6.48
d. 10
20. In a study of speed of a car covered a distance travelled to a college by a
student, a harmonic mean yielded 16.7442 miles/ hour. After the mean was
calculated that one value of 16 misprinted mistakenly and true value was 10.
Then the true Harmonic mean is equal to.
a. 10.7442
b. 13
c. 15.7442
d. 13.846
21. The Box and Whisker Plots for the weights (Pounds) and height (inches) of
482 applicants for admission in a cadet college at 2014 are given below
Which of the following is an accurate comparison of the box plots?
a. On both plots, the median is exactly half way between the
Lower and Upper Quartiles. (Yes or No)
b. Weights of cadets has a smaller range & heights of cadets has a
larger IQR (Inter Quartile Range = 𝑄3 − 𝑄1) (Yes or No)
c. Inter Quartile Range of weights of cadets is equal to
_____________ and Inter Quartile Range of heights of cadets
is equal to ___________
22. Consider the following two data sets.
Data Set I: 4
8
15
9
11
Data Set II 8
16
30
18
22
Notice that each value of the second data set is obtained by multiplying the
corresponding value of the first data set by 2. The mean and variance of Data
Set I is calculated as 9.4 and 4.03732 respectively. The mean and variance of
Data Set II will be equal to
a. Mean = 2 × 9.4 and Variance = 4.03732
b. Mean = 2 × 9.4 and Variance = 2 × 4.03732
c. Mean = 2 × 9.4 and Variance = 4 × 4.03732
d. Mean = 4 × 9.4 and Variance = 4 × 4.03732
23. Refer to the graph below
Frequency polygone
175
158
62
1
0.395
55
5
0.615
0.835
1.055
1.275
1.495
8
13
1.715
1.935
0
2.155
1
2.375
1
2.595
A. Mode expense rate is
a. 0.835
b. 1.055
c. 1.275
d. 0.945
B. Median expense rate is
a. 0.835
b. 1.055
c. 1.275
d. 0.945
C. Is this data skewed in any direction?
a. Yes, positively skewed
c. No, symmetrical
b. Yes, negatively skewed
d. Not symmetrical nor skewed
Q.2 Short questions
1. Two data sets of weights (Pounds) of 469 and 478 applicants for admission in a
cadet college at 2012 and 2013 respectively are given below
1. Find the missing values in the table below.
Class
Mean
Variance
Median
Q1
Q3
Minimum
Maximum
2012
2013
219.7741
26.5871
219.3646
26.2187
2. Indicate the skewness or symmetry for both classes. Which class
contains outlier(S). Identify it?
3. Indicate in which year the cadets have more homogenous weights?
2. The histogram and excel outcome of descriptive statistics of ten Year return for
funds of 479 retired police officers for year 2016 are given below
Column1
Mean
Standard Error
Median
Mode
7.217870564
0.082967258
7.31
8.89
Bin /
upper
class
limits
0.3
1.71
3.12
4.53
Frequency
Cumulative %
1
4
5
16
0.21%
1.04%
2.09%
5.43%
Standard
1.81582711
Deviation
Sample Variance 3.297228092
Kurtosis
1.448602426
Skewness
0.458405475
Range
14.1
Minimum
-1.1
Maximum
13
Sum
3457.36
Count
479
5.94
82
22.55%
7.35
8.76
138
147
51.36%
82.05%
10.17
65
95.62%
11.58
12.99
14.4
More
17
3
1
0
99.16%
99.79%
100.00%
100.00%
1. Complete a frequency distribution and draw a histogram for a given
frequency distribution
2. Detect any outlier (s) in this data set if it exist in your opinion
3. Find a better summary measure of central tendency whether it is the
mean or the median? Explain.
4. Identify the symmetry and skewness of 10 year returns of 479 officers.
5. Find the (approximate) value of the 95th percentile. Give a brief
interpretation of this percentile.
6. Indicate is there any consistency in 10 year returns of 479 officers?
7. Find the percentages of the given data values that fall within 1.5 standard
deviation of the mean. (𝑋̅ ± 1.5 𝑆. 𝐷)
3. The geometric mean of four numbers were calculated as 107.8482. After it was
noted that the third value 111.3 wrongly considered instead of 110.25 value.
Find the true geometric mean?
4. A man travels by a car for 4 days. He travelled for 10 hours each day. He drove
on the first day at the rate of 45 km per hour, second day at 40 km per hour, third
day at the rate of 38 km per and the fourth day at the rate of 37 km per hour.
Which average , harmonic mean or arithmetic mean or geometric mean will give
average speed? why?
5. A sample of restaurants in a large city revealed that the average price of a cup of
coffee was 58 cents, and the standard deviation was 8 cents. Three of the
restaurants charged 50, 45, and 60 cents. Find Z-scores for these restaurants.
6. Jane works for a company whose employees had an average income this past
year of $28,000 with a standard deviation of $3000. How much did Jane earn
this past year if her z-score is -0.8?
7. In a marketing experiment a supermarket chain of three stores sold lettuce, on a
certain day, at a different price in each of its stores.
Store
Head
Price (cents)
1
75
98
2
125
88
2
300
69
a. How much was the average price per head of lettuce sold by the supermarket
chain?
b. How many additional heads of lettuce must be sold at 98 cents a head to raise
the mean price of lettuce sold that day by the supermarket chain to 80 cents
per head ?
8. The histogram and excel outcome of descriptive statistics of Assets for funds of
479 retired police officers for year 2016 are given below
Column1
Mean
1644.716305
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
128.1842876
547.73
779.93
2805.450115
7870550.35
9.85459805
2.968398968
19384.17
4.13
19388.3
787819.11
479
Bin /
upper
class
limits
1942.546
3880.963
5819.38
7757.797
9696.214
11633.631
13572.048
15510.465
17448.882
19387.29
21325.707
More
Frequency
Cumulative %
371
57
13
10
14
3
5
5
0
0
1
0
77.45%
89.35%
92.07%
94.15%
97.08%
97.70%
98.75%
99.79%
99.79%
99.79%
100.00%
100.00%
1. Complete a frequency distribution and draw a histogram for a given
frequency distribution
2. Detect any outlier (s) in this data set if it exist in your opinion
3. Find a better summary measure of central tendency whether it is the
mean or the median? Explain.
4. Identify the symmetry and skewness of this data.
5. Find the (approximate) value of the 97th percentile. Give a brief
interpretation of this percentile.
6. Indicate is there any homogeneity of Assets for funds of 479 retired
police officers for year 2016?
9. One Year return for funds of 479 retired police officers for year 2016 collected
and this information has been summarised on the box plots below.
1. Describe the five number value summary
2. Is the data set skewed in any direction? If yes, detect it as skewed to the right or
to the left? Does this data set contain any outliers? If yes then identify it.
10. The histogram and excel outcome of descriptive statistics of heights (inches) of
439 applicants for admission in a cadet college at 2000 are given below
Bin /
Cumulative
Heights (Inches)
upper
Frequency
%
class limits
Mean
78.93849658
65
2
0.46%
Standard Error
0.18088487
68
0
0.46%
Median
79
71
8
2.28%
Mode
81
74
50
13.67%
Standard
3.789958918
77
84
32.80%
Deviation
Sample Variance 14.3637886
80
117
59.45%
Kurtosis
0.516420999
83
142
91.80%
Skewness
-0.395616882
86
30
98.63%
Range
28
89
4
99.54%
Minimum
63
92
2
100.00%
Maximum
91
More
0
100.00%
Sum
34654
Count
439
1. Complete a frequency distribution and draw a histogram for a given
frequency distribution
2. Detect any outlier (s) in this data set if it exist in your opinion
3. Find a better summary measure of central tendency whether it is the
mean or the median? Explain.
4. Identify the symmetry and skewness of this data.
5. Find the (approximate) value of the 95th percentile. Give a brief
interpretation of this percentile.
6. Indicate is there any homogeneity in heights of 439 cadets?
11. How much does the typical American family spend on average to go away on
vacation each year? Twenty-five randomly selected households reported the
following vacation expenditures (rounded to the nearest hundred dollars) during
the past year:
2500
500
800
0
100
0
200
2200
0
200
0
1000
900
321,400
500
500
100
0
8200
900
0
1700
1100
600
3400
a. Find mean, median and mode of given data.
b. Label the best measure of central tendency to answer the original question?
12. The histogram and excel outcome of descriptive statistics of heights (Inches) of
441 applicants for admission in a cadet college at 2014 are given below
Column1
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
78.95464853
0.180517434
79
81
3.790866107
14.37066584
0.228646046
-0.354535468
28
63
91
34819
441
Bin / upper
class limits
65
68
71
74
77
80
83
86
89
92
More
Frequency
1
0
9
52
83
120
139
32
3
2
0
Cumulative
%
0.23%
0.23%
2.27%
14.06%
32.88%
60.09%
91.61%
98.87%
99.55%
100.00%
100.00%
1. Complete a frequency distribution and draw a histogram for a given
frequency distribution
2. Detect any outlier (s) in this data set if it exist in your opinion
3. Find a better summary measure of central tendency whether it is the
mean or the median? Explain.
4. Identify the symmetry and skewness of this data.
5. Find the (approximate) value of the 90th percentile. Give a brief
interpretation of this percentile.
6. Indicate is there any homogeneity in heights of 441 cadets?
7. Find the percentages of the given data values that fall within 0.5 standard
deviation of the mean. (𝑋̅ ± 0.5 𝑆. 𝐷)
The End
SUBMISSION DATE
04/04/2022