Which of the following has the same mean, median and mode?
(a) 6, 2, 5, 4, 3, 4, 1
(b) 4, 2, 2, 1, 3, 2, 3
(c) 2, 3, 7, 3, 8, 3, 2
(d) 4, 3, 4, 3, 4, 6, 4

Solution:

We have to determine which data has the same mean, median and mode.

We know, mean = sum of all observation/number of observation

When the given data is arranged in ascending (or descending) order, then the middle most observation is the median of the data.

Mode is the observation that occurs most frequently in the data.

(a) Considering 6, 2, 5, 4, 3, 4, 1

Arranging the data in ascending order, we get

1, 2, 3, 4, 4, 5, 6

Mean = (6 + 2 + 5 + 4 + 3 + 4 + 1)/7 = 25/7 = 3.57

Median = 4

Mode = 4

(b) Considering 4, 2, 2, 1, 3, 2, 3

Arranging the data in ascending order, we get

1, 2, 2, 2, 3, 3, 4

Mean = (4 + 2 + 2 + 1 + 3 + 2 + 3)/7 = 17/7 = 2.42

Median = 2

Mode = 2

(c) Considering 2, 3, 7, 3, 8, 3, 2

Arranging the data in ascending order, we get

2, 2, 3, 3, 3, 7, 8

Mean = (2 + 2 + 3 + 3 + 3 + 7 + 8)/7 = 28/7 = 4

Median = 3

Mode = 3

(d) Considering 4, 3, 4, 3, 4, 6, 4

Arranging the data in ascending order, we get

3, 3, 4, 4, 4, 4, 6

Mean = (3 + 3 + 4 + 4 + 4 + 4 + 6)/7 = 28/7 = 4

Median = 4

Mode = 4

Therefore, the mean, median and mode is same in the data 4, 3, 4, 3, 4, 6, 4

✦ Try This: Find the mean of the data 2, 3, 7, 3, 8, 3, 4

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 3

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NCERT Exemplar Class 7 Maths Chapter 3 Problem 16

Which of the following has the same mean, median and mode? (a) 6, 2, 5, 4, 3, 4, 1 (b) 4, 2, 2, 1, 3, 2, 3 (c) 2, 3, 7, 3, 8, 3, 2 (d) 4, 3, 4, 3, 4, 6, 4

Summary:

4, 3, 4, 3, 4, 6, 4 has the same mean, median and mode.

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☛ Related Questions:

• The difference between the highest and the lowest observations of a data is called _________. Fill i . . . .
• The mean of a data is defined as _________. Fill in the blanks to make the statement true
• In a set of observations, the observation that occurs the most often is called _________. Fill in th . . . .