Class 9 Mean and Median Mock Test (ICSE)

Topics in Mean and Median

• Mean of ungrouped data
• Mean of ungrouped frequency distribution
• Median of ungrouped data
• Properties of mean

Mean and Median practice questions with answers

1. Q1Multiple choice·1 mark
   If the mean of the following distribution is $4$, find the value of $p$. $x$: $2, 4, 6, 8$ $f$: $3, 2, p, 1$

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

   1. Correct option: (a) $1$. Using $\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}$, we get $\frac{2(3) + 4(2) + 6(p) + 8(1)}{3 + 2 + p + 1} = 4$, which simplifies to $\frac{6 + 8 + 6p + 8}{6 + p} = 4 \implies \frac{22 + 6p}{6 + p} = 4 \implies 22 + 6p = 24 + 4p \implies 2p = 2 \implies p = 1$.+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   Find the mean of the first five prime numbers.

   1. (a)$4.8$
   2. (b)$5.6$
   3. (c)$5.2$
   4. (d)$6.0$
   Show answer and step marks

   1. Correct option: (b) $5.6$. The first five prime numbers are $2, 3, 5, 7, 11$, and their mean is $\frac{2 + 3 + 5 + 7 + 11}{5} = \frac{28}{5} = 5.6$.+1

   Answer: (b)
3. Q3Multiple choice·1 mark
   If each observation of a set of data is increased by $5$, then the mean of the new observations:

   1. (a)is increased by $5$
   2. (b)is multiplied by $5$
   3. (c)remains unchanged
   4. (d)is divided by $5$
   Show answer and step marks

   1. Correct option: (a) is increased by $5$. By the properties of mean, if a constant $c$ is added to each observation, the mean also increases by $c$.+1

   Answer: (a)
4. Q4Multiple choice·1 mark
   The median of the observations $11, 12, 14, 18, x+2, x+4, 30, 32, 35, 41$ arranged in ascending order is $24$. Find the value of $x$.

   1. (a)$22$
   2. (b)$21$
   3. (c)$19$
   4. (d)$20$
   Show answer and step marks

   1. Correct option: (b) $21$. Since $n = 10$ (even), the median is the average of the 5th and 6th terms: $\frac{(x+2) + (x+4)}{2} = 24 \implies 2x + 6 = 48 \implies 2x = 42 \implies x = 21$.+1

   Answer: (b)

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