Statistics (Mean Median Mode)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #21

State true or false.
(i) For all data, `\sum_{i=1}^n (x_i - \bar{x}) = 0`.
(ii) Mean and median of the following data are equal: 5, 3, 9, 6, 7.
(iii) If `n` is an odd number, then `(n+1)/2`-th term is the median.
(iv) If `n` is an even number, then average of `n/2` th and `(n/2-1)` th observation is the median of that data.
(v) Median of the data `2, 3, 9, 10, 9, 3, 9` is 10.
(vi) The median is always one of the numbers in a data.
(vii) An ogive is always a straight line graph.
(viii) Mode of the data `2, 3, 3, 2, 5, 2, 3, 6, 5` is 6.
(ix) There can be multiple modes for a given data set.
(x) There can be no mode for a given data set.

Question No: #22

If `\sum_{i=1}^5 x_i=4` and `\sum_{i=1}^5 x_i^2=12`, then find the value of `\sum_{i=1}^5 2x_i(x_i-3)`.
Ans: `0`
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Question No: #23

If `u_i = \frac{x_i - 10}{5}, \sum f_iu_i=30` and `\sum f_i = 50`, then find the value of `\bar{x}`.

Question No: #24

If the mean of a frequency distribution is `8.1`, `\sum f_ix_i = 132+5k, \sum f_i = 20`, then find the value of `k`.

Question No: #25

The frequency of three numbers 12, 15 and 20 are `x+2`, `x` and `x-1` respectively. If the mean of this data is 14.5, find `x`.

Question No: #26

Mean of the 10 members is 30. Later on, it was observed that numbers 20, 21 are wrongly taken as 15, 17 respectively. Find the correct mean.
Ans: 30.9
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Question No: #27

If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by -
(a) 2, (b) 1.5, (c) 1, (d) 0.5
Ans: (d) 0.5
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Question No: #28

The numbers 6, 8, 10, 12, 13 and `x` are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of `x`.

Question No: #29

If the mean of the data `x-3, x-1, 7, x, 2x-1, 3x-5` is 3.5, then find its median.
Ans: 2.5
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Question No: #30

If the numbers `11, 12, 14, x-2, x+4, x+9, 32, 38, 47` are arranged in ascending order and their median is `24`, what is the value of `x`?