TUTORIAL SHEET 1
STATISTICS
1. Draw histograms and frequency polygons for the following data
a. The average rainfall in the last 90 days in Ireland
Average Rainfall (mms)
days
0–5
7
6 – 10
10
11 – 15
15
16 – 20
21
21 – 25
9
26 – 30
0
31 – 35
11
36 – 40
6
41 – 45
7
46 – 50
3
51 – 55
1
b. The share price of 140 companies on a given day
Price in €
Number of companies
0 – 60
72
61 – 120
23
121 – 180
7
181 – 240
6
241 – 300
5
301 – 360
9
361 – 420
12
421 – 480
3
481 – 540
3
Comment on the suitability of the class interval size chosen for this data
2. Construct frequency distributions and hence draw histograms for the following sets of data
a. The birth weights of 30 children (in kgs) born on a given day
3.25, 2.98, 3.01, 3.35, 3.71, 3.82, 3.11, 2.65, 2.51, 4.01, 3.79, 3.81, 4.21, 4.75, 3.21,
4.17, 4.34, 3.72, 2.78, 2.61, 3.21, 3.73, 4.01, 4.56, 3.45, 3.17, 3.93, 4.27, 3.81, 4.11
b. The time taken (in seconds) by 25 students to complete an online quiz
10.01, 12.56, 13.98, 15.21, 9.45, 11.22, 17.34, 15.34, 12.32, 21.89,
7.23, 8.57, 10.43, 12.45, 16.89, 15.32, 17.46, 20.45, 19.34, 16.34,
8.79, 12.34, 15.48, 23.12, 16.77
3. For the tables in questions 1 and 2 above construct cumulative frequency tables and draw
the corresponding ogives.
Pam O’Brien © 2012
Statistical Data Analysis
Section 1 - Statistics
Page: 1 of 2
4. For the tables of data in question 2 above calculate the
a. 20th percentile
b. 65th percentile
5. For the following sets of data calculate the mean, mode, median
a. 35, 42, 56, 39, 38, 41, 40, 35, 43, 36
b. 11, 14, 7, 8, 12, 11, 11, 17, 9
c. 10.01, 12.56, 13.98, 15.21, 9.45, 11.22, 17.34, 15.34, 12.32, 21.89,
6. For the following sets of data calculate the range, the mean deviation, the semi-interquartile
range and the standard deviation
a. 35, 42, 56, 39, 38, 41, 40, 35, 43, 36
b. 11, 14, 7, 8, 12, 11, 11, 17, 9
7. Calculate
a. The standard scores achieved in an exam with mean 59 and standard deviation 17 if
the marks achieved were
i. 68
ii. 79
iii. 41
b. The actual marks achieved in an exam with mean 48 and standard deviation 19 if the
standard scores achieved were
i. 1.0
ii. -0.65
iii. -2.1
c. Find the mean and standard deviation of exam grades if standard scores of 0.7 and 1.2 correspond to 65 and 42 respectively
Pam O’Brien © 2012
Statistical Data Analysis
Section 1 - Statistics
Page: 2 of 2