Finding the mean median mode practice problems

As neither of the classes have any repeated scores, we can’t use the mode. Therefore, let’s look at median,

Order Class A: 35, 36, 47, 64, 66, 76, 84, 89, 95

Middle score: 66

Order Class B: 50, 51, 56, 59, 60, 63, 66, 70, 84

Middle score: 60

So, Class A has a higher median.

Now, let’s look at range to consider the spread of data:

Class A range: 95-35=60

Class B range: 84-50=34

Class A has a bigger range.

In conclusion, Class A generally has higher scores, with both the mean and median being higher than class B. Class B’s scores are more concentrated and less spread out than Class A.

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PRACTICE PROBLEMS ON MEAN MEDIAN AND MODE

Problem 1 :

Find the (i) mean  (ii) median  (iii) mode for each of the following data sets :

a)  12, 17, 20, 24, 25, 30, 40

b)  8, 8, 8, 10, 11, 11, 12, 12, 16, 20, 20, 24

c)  7.9, 8.5, 9.1, 9.2, 9.9, 10.0, 11.1, 11.2, 11.2, 12.6, 12.9

d)  427, 423, 415, 405, 445, 433, 442, 415, 435, 448, 429, 427, 403, 430, 446, 440, 425, 424, 419, 428, 441

Solution

Problem 2 :

Consider the following two data sets :

Data set A : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 12

Data set B : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 20

a)  Find the mean for both Data set A and Data set B.

b)  Find the median of both Data set A and Data set B.

c)  Explain why the mean of Data set A is less than the mean of Data set B.

d)  Explain why the median of Data set A is the same as the median of Data set B

Solution

Problem 3 :

The table given shows the result when 3 coins were tossed simultaneously 40 times. The number of heads appearing was recorded.

Calculate the :   a)  mean     b)  median     c)  mode

Solution

Problem 4 :

The following frequency table records the number of text messages sent in a day by 50 fifteen-years-olds

a)  For this data, find the : (i) mean   (ii)  median   (iii)  mode

b)  construct a column graph for the data and show the position of the measures of centre (mean, median and mode) on the horizontal axis.

c)  Describe the distribution of the data.

d)  why is the mean smaller than the median for this data ?

e)  which measure of centre would be the most suitable for this data set ?

Solution

Problem 5 :

The frequency column graph alongside gives the value of donations for an overseas aid organisation, collected in a particular street.

a)  construct the frequency table from the graph.

b)  Determine the total number of donations.

c)  For the donations find the :  (i)  mean   (ii)  median   (iii)  mode

d) which of the measures of central tendency can be found easily from the graph only ?

Solution

Problem 6 :

Hui breeds ducks. The number of ducklings surviving for each pair after one month is recorded in the table.

a)  Calculate the : (i)  mean   (ii)  median   (iii) mode

b)  Is the data skewed ?

c)  How does the skewness of the data affect the measures of the middle of the distribution ?

Solution

Answers 

(1)

Mean

Median

Mode

(a)

24

24

No mode

(b)

13.33

11.5

8

(c)

10.32

10

11.2

(d)

428.57

428

415 and 427

(2)

Set A

Mean  =  7.73

Median  =  7

Set B

Mean  =  8.45

Median  =  7

(c)  the mean of A is less than the mean of B.

(d)  median is the same.

(3)  (a)  Mean  =  1.4    (b)  median  =  1  (c)   mode  =  1

(4)  

(a)  (i)  Mean  =  5.74  (ii)   median  =  7  (iii)  mode  =  8

(b) 

(c)   bimodal data.

(d)

The mean takes into account the full range of numbers of text messages and is affected by extreme values. Also, the value which is lower than the median is well below it.

(e)  The median

(5)  

(a)

(b)  ∑f  =  30

(c)  (i)  Mean  =  $2.9  (ii)  median  =  $2  (iii)  mode  =  $2

(6)  

(a)  (i)  Mean  =  4.25   (ii)  median  =  5   (iii)  mode  =  5

c)  By observing the graph, the mean is less than the median and mode.

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