A) CitiBank recorded the number of customers to use a downtown ATM during the noon hour
on 32 consecutive workdays. (a) Use Excel or MegaStat to find the mean, median, and mode.
(b) Do these measures of central tendency agree? Explain. (c) Are the data symmetric or
skewed? If skewed, which direction? (d) Note strengths or weaknesses of each statistic of
central tendency for the data.
x
sorted
25
39
18
33
37
32
26
9
23
21
34
16
26
26
18
32
30
19
31
35
40
27
35
42
25
32
21
15
26
25
33
24
9
15
16
18
18
19
21
21
23
24
25
25
25
26
26
26
26
27
30
31
32
32
32
33
33
34
35
35
37
39
40
42
Sum
n
mean
median
mode
875
32
27.34375
26
26
class
8-14
15-21
22-28
29-35
36-42
total
frequency
1
7
10
10
4
32
Mean = sum of the observations / number of observations = 875/32 = 27.34375
Median = middle most observation when the the observations are sorted in the order of magnitude.
There are 32 observations. The median is the mean of the two middle most observations. The mean
of the 16th and 17th observations when the observations are arranged in the order of magnitude.
Median = (26+26)/2 = 52/2 =26
Mode is the most frequently occurring observation.
x
9
15
16
18
19
21
23
24
25
26
27
30
31
32
33
34
35
37
39
40
42
Total
frequency
1
1
1
2
1
2
1
1
3
4
1
1
1
3
2
1
2
1
1
1
1
32
The observation with maximum frequency is 26.
Therefore the mode is 26.
Mean = 27.34375
Median = Mode = 26
The median and the mode are equal. But the mean is different from the median and mode.
But difference is not much. If the distribution is perfectly symmetric, then all these measures will be
exactly equal. Here the distribution is approximately symmetric.
frequency
12
10
8
6
frequency
4
2
0
8-14
15-21
22-28
29-35
36-42
The distribution is almost symmetric. This can be seen from the graph. A light positive skewness can
be detected from the fact that the mean is to the right of the median and mode.
Comparison of mean median and mode.
It must be understood that no one average can be regarded as best for all circumstances. The
following considerations influence the selection of an appropriate average:
1. The purpose which the average is designed to serve.
2. Would the average be used for further computations?
3. The type of data available.
On occasions, it may even be advisable to work out more than average.
Median
The median is generally the best average in open- end grouped distributions.
Mode
The mode can be used to describe qualitative data.
Mean
The mean depends on all the observations and is amenable to further algebraic manipulations.