Question

The table below shows the scores of a group of students on a 10-point quiz. test score frequency 3 3 4 3 5 3 6 1 7 3 8 1 9 5 10 5 the mean score on this test is: the median score on this test is

Answer 1

Answer:

Mean of data is 4.75 and median is 4.5

Step-by-step explanation:

Given,

Score of group of students = 3, 3, 4, 3, 5, 3, 6, 1, 7, 3, 8, 1, 9, 5, 10, 5

We know,

To find the mean, We add all the scores and divide by total number of scores

Sum of all scores = 3 + 3 + 4 + 3 + 5 + 3 + 6 + 1 + 7 + 3 + 8 + 1 + 9 + 5 + 10 + 5

Sum of scores = 76

Total number of scores = 16

So,

Mean = 76 / 16

Mean = 4.75

Now,

To find Median we place all the numbers in order and find the middle number.

Two cases exist :

Case 1 :

When the number of observations (n) is odd, the median is the value of the

$(\frac{n+1}{2} )^{th}$

Case 2 :

When the number of observations (n) is even, the median is the average of the  $(\frac{n}{2} )^{th}$ and $(\frac{n}{2} + 1 )^{th}$

So,

We will first arrange the scores in order :

1, 1, 3, 3, 3, 3, 3, 4, 5, 5, 5, 6, 7, 8, 9, 10

So since the number of observation is even , that is, 16

So we will apply case 2,

$(\frac{n}{2} )^{th}$ = 8th observation = 4

$(\frac{n}{2} + 1 )^{th}$ = 9th observation = 5

Mean of 4 and 5 = ( 4 + 5 ) / 2

= 9 / 2

= 4.5

So,

Median = 4.5

Hence ,

Mean of data is 4.75 and median is 4.5