Class 10 Mean, Median, Quartiles and Mode Mock Test (ICSE)

Topics in Mean, Median, Quartiles and Mode

• Mean of grouped data by direct, short-cut and step-deviation methods
• Median of ungrouped data
• Quartiles and interquartile range
• Mode of ungrouped data

Mean, Median, Quartiles and Mode practice questions with answers

1. Q1Multiple choice·1 mark
   For a given distribution, if the lower quartile $Q_1$ is $18$ and the upper quartile $Q_3$ is $54$, then the interquartile range is:

   1. (a)$54$
   2. (b)$72$
   3. (c)$36$
   4. (d)$18$
   Show answer and step marks

   1. Correct option: (c) $36$. Interquartile range is calculated as $Q_3 - Q_1 = 54 - 18 = 36$.+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   If the mean of $n$ observations $x_1, x_2, \dots, x_n$ is $\bar{x}$, then the mean of $x_1 + a, x_2 + a, \dots, x_n + a$ is:

   1. (a)$\bar{x} + a$
   2. (b)$\bar{x}$
   3. (c)$a\bar{x}$
   4. (d)$\bar{x} - a$
   Show answer and step marks

   1. Correct option: (a) $\bar{x} + a$, as adding a constant to every observation increases the mean by the same constant.+1

   Answer: (a)
3. Q3Multiple choice·1 mark
   What is the mode of the following ungrouped data: $14, 25, 14, 28, 35, 14, 38, 42, 25$?

   1. (a)$38$
   2. (b)$25$
   3. (c)$14$
   4. (d)$42$
   Show answer and step marks

   1. Correct option: (c) $14$, since it has the highest frequency (appears 3 times).+1

   Answer: (c)
4. Q4Multiple choice·1 mark
   Find the median of the first 7 prime numbers: $2, 3, 5, 7, 11, 13, 17$.

   1. (a)$5$
   2. (b)$13$
   3. (c)$11$
   4. (d)$7$
   Show answer and step marks

   1. Correct option: (d) $7$. Since there are 7 observations arranged in ascending order, the median is the $(7+1)/2$-th term, which is the 4th term, i.e., $7$.+1

   Answer: (d)

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