
The

Answer to Problem 1TP
The mean of the given data is 28.375, the median is 25.5 and the mode is 23.
Explanation of Solution
The given information represents the set of 40 reading scores.
31 | 32 | 43 | 42 |
24 | 34 | 25 | 44 |
23 | 43 | 24 | 36 |
25 | 41 | 23 | 28 |
14 | 21 | 24 | 17 |
25 | 23 | 44 | 21 |
13 | 26 | 23 | 32 |
12 | 26 | 14 | 42 |
14 | 31 | 52 | 12 |
23 | 42 | 32 | 34 |
Calculation:
The formula for mean is given below:
Substitute 1,135 for
Thus, the mean of the given data is 28.375.
Arrange the given data in ascending order, to find the median of the given data.
S. No | Values | S. No | Values | S. No | Values | S. No | Values |
1 | 12 | 11 | 23 | 21 | 26 | 31 | 36 |
2 | 12 | 12 | 23 | 22 | 26 | 32 | 41 |
3 | 13 | 13 | 23 | 23 | 28 | 33 | 42 |
4 | 14 | 14 | 23 | 24 | 31 | 34 | 42 |
5 | 14 | 15 | 24 | 25 | 31 | 35 | 42 |
6 | 14 | 16 | 24 | 26 | 32 | 36 | 43 |
7 | 17 | 17 | 24 | 27 | 32 | 37 | 43 |
8 | 21 | 18 | 25 | 28 | 32 | 38 | 44 |
9 | 21 | 19 | 25 | 29 | 34 | 39 | 44 |
10 | 23 | 20 | 25 | 30 | 34 | 40 | 52 |
The total number of terms is 40, which is an even number.
The formula for median when n is even is given below:
Substitute 40 for n in the above equation,
The 20th term is 25 and 21st term is 26 when the data is arranged in the ascending order.
Substitute 25 for
Thus, the median of the given data is 25.5.
Mode:
The value in data set which occurs maximum times is called mode.
The frequency of the data is tabulated below:
Value | Frequency | Value | Frequency |
12 | 2 | 31 | 2 |
13 | 1 | 32 | 3 |
14 | 3 | 34 | 2 |
17 | 1 | 36 | 1 |
21 | 2 | 41 | 1 |
23 | 5 | 42 | 3 |
24 | 3 | 43 | 2 |
25 | 3 | 44 | 2 |
26 | 2 | 52 | 1 |
28 | 1 | - | - |
From the above table it is noticed that the highest frequency is 5 for 23.
Thus, the mode of the given data is 23.
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Chapter 2 Solutions
Statistics for People Who (Think They) Hate Statistics, Salkind, Without CD
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