Question

What is the mean, median, mode and midrange of this chart?

Answer 1

According to this chart, the mean of the data is 14, the median is 12.5, the mode is 15, and the midrange is 12.5.

How the mean, median, mode, and midrange are determined:

The mean is the sum of all the scores divided by the total number of scores.

The sum of all the scores = 252 (9*0 + 2*10 + 3*11 + 4*12 + 5*13 + 1*14 + 3*15 + 0*16)

The number of scores = 18 scores

The mean = 252/18 = 14

The median represents the middle score arranged in order.

The middle scores are 12 and 13.

The median = 12.5 (12+13)/2

The mode refers to the most frequently appearing or occurring score.

Score 15 appears three times.

The mode = 15.

The midrange gives the average of the highest and lowest scores.

The highest score = 13

The lowest score = 10

The midrange = 12.5 (13+10)/2

The data points displayed on the graph are:

Frequency Score

0 9

2 10

3 11

4 12

5 13

1 14

3 15

0 16

Answer 2

The values of the central tendency are

Mean is 12.5

Median is 13.5

Mode is 13

Midrange is 12.5

How the values were calculated

From the graph

x f

10 2

11 3

12 4

13 5

14 1

15 3

Data: 10, 11, 12, 13, 14, 15

Frequency: 2, 3, 4, 5, 1, 3

Mean = sum (x f)/sum f

Mean} = 10* 2) + (11 *3) + (12 *4) + (13 *5) + (14* 1) + (15* 3)/(2 + 3 + 4 + 5 + 1 + 3)

= (20 + 33 + 48 + 65 + 14 + 45)/18

= 225/18

= 12.5

Median:

The median is the middle number

Nth/2 number

=18/2 = 9th number and 10th numbers since frequency is even.

= (13+14)/2

= 27/2 = 13.5

Mode:

The mode is the value(s) with the highest frequency. 13 has the highest frequency of 5, 13 is the mode.

Midrange:

The midrange is the average of the maximum and minimum values.

Midrange =Maximum value} + Minimum value/2

Midrange = (15 + 10)/2

= 25/2

= 12.5

Therefore,the values of the central tendency are

Mean is 12.5

Median is 13.5

Mode is 13

Midrange is 12.5