Statistics for People Who (Think They) Hate Statistics
Statistics for People Who (Think They) Hate Statistics
6th Edition
ISBN: 9781506333830
Author: Neil J. Salkind
Publisher: SAGE Publications, Inc
Question
Chapter 2, Problem 1TP
To determine

The mean, median and mode for the set of 40 chemistry final scores.

Expert Solution & Answer
Check Mark

Answer to Problem 1TP

The mean of the chemistry final scores is 87.55, median of the chemistry final scores is 88, mode of the chemistry final scores is 94.

Explanation of Solution

The given data set of 40 scores that consists of chemistry final marks is given below:

93859977
94998676
95999784
91897787
97838098
75948185
78928994
76949694
90798094
77868381

Calculation:

The formula to calculate the mean is,

X¯=1nXn=X1+X2+X3+...+Xnn (1)

Where,

  • X is the number of final scores.
  • n is the total number of final scores.

The sum of the 40 final scores is given below.

140X={93+94+95+91+97+75+78+76+90+77+85+99+99+89+83+94+92+94+79+86+99+86+97+77+80+81+89+96+80+83+77+76+84+87+98+85+94+94+92+81}=3,502

Substitute 3502 for 140X and 40 for n in equation (1),

Mean=3,50240=87.55

Thus, the mean is 87.55.

Median:

For calculation of median, arrange the data in ascending or descending order. Now data is arranged in descending order as shown below:

99999998979796959494
94949493929291908989
87868685858483838181
80807978777777767675

The formula to calculate the median for even data is shown below.

Median=(n2)thterm+(n2+1)thterm2

The total number of terms in the data is 40 so, substitute 40 for n in the above formula.

Median=(402)thterm+(402+1)thterm2=(20)thterm+(21)stterm2 (2)

20thterm from the arranged data is 89 and the 21stterm is 87.

Substitute 89 for 20thterm and 87 for 21stterm in equation (2).

20thterm+21stterm2=89+872=1762=88

Thus, the median is 88.

Mode:

For calculation of mode, check the number that occurs most frequent. Since, 94 occur for 5 times in the table, thus 94 is the mode.

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