Answered: Find the mean, median, and mode of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Find the mean, median, and mode of the following statistic studentsʹ test scores:

96, 99, 92, 96, 89, 97, 96, 90, 91, 94

Question 15 options:

	96
	95
	94

1.	Mean
2.	Median
3.	Mode

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

Expert Solution

Step 1

The mean of the statistic students test scores is,

$\begin{array}{rcl} M e a n & = & \frac{\sum_{} X}{n} \\ = & \frac{96 + 99 + 92 + 96 + 89 + 97 + 96 + 90 + 91 + 94}{10} \\ = & \frac{940}{10} \\ = & 94 \end{array}$

Thus, the mean of the statistic students test scores is 94.

The statistic students test scores in the ascending order is 89, 90, 91, 92, 94, 96, 96, 96, 97, 99.

The position of median value for even sample size is,

$\begin{array}{rcl} M e d i a n & = & {[\frac{50 (n + 1)}{100}]}^{t h} D a t a v a l u e \\ = & {[\frac{50 (10 + 1)}{100}]}^{t h} D a t a v a l u e \\ = & 5 . 5^{t h} D a t a v a l u e \end{array}$

The median (Second quartile) is,

$\begin{array}{rcl} M e d i a n & = & 5^{t h} D a t a v a l u e + 0.5 (6^{t h} D a t a v a l u e - 5^{t h} D a t a v a l u e) \\ = & 94 + 0.5 (96 - 94) \\ = & 94 + 1 \\ = & 95 \end{array}$

Thus, the median of the statistic students test scores is 95.

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