Statistics CBSE Class 9 Mathematics Worksheets Set 04

Practice Set

Question 1. The mean of 40 observations was 160. On rechecking, 165 was found to have been wrongly copied as 125. Find the correct mean.
Answer:
Incorrect sum \( =40\times160=6400 \).
Correct sum \( =6400-125+165=6440 \).
Correct mean \( =\frac{6440}{40}=161 \).

Question 2. The mean of \( 5,7,p,11,15,17,20 \) is \( 12 \). Find \( p \).
Answer:
\( \frac{5+7+p+11+15+17+20}{7}=12 \), so \( 75+p=84 \).
\( p=9 \).

Question 3. If the mean of 5 observations is 15 and the mean of another 10 observations is 20, find the mean of all 15 observations.
Answer:
Sum of the first five \( =5\times15=75 \); sum of the other ten \( =10\times20=200 \).
Mean \( =\frac{275}{15}=18.33 \) (that is \( \frac{55}{3} \)).

Question 4. Find the mean of the distribution \( x:10,30,50,70,89 \) with frequencies \( f:7,8,10,15,10 \).
Answer:
\( fx \) values: 70, 240, 500, 1050, 890, with total \( 2750 \); \( N=50 \).
Mean \( =\frac{2750}{50}=55 \).

Question 5. Find the missing frequencies \( f_1,f_2 \) in the distribution \( x:0,1,2,3,4,5 \), \( f:46,f_1,f_2,25,10,5 \), given that the total frequency is 200 and the mean is 1.46.
Answer:
\( 86+f_1+f_2=200 \), so \( f_1+f_2=114 \).
\( \sum fx=f_1+2f_2+75+40+25 \) and this equals \( 1.46\times200=292 \), so \( f_1+2f_2=152 \).
Subtracting the first equation, \( f_2=38 \) and \( f_1=76 \).

Question 6. Find the median of the data \( 25,34,31,23,22,26,35,28,20,32 \).
Answer:
In ascending order: 20, 22, 23, 25, 26, 28, 31, 32, 34, 35 (10 values).
Median \( =\frac{26+28}{2}=27 \).

Question 7. Find the median of \( 19,25,59,48,35,31,30,32,51 \). What is the new median if 25 is replaced by 52?
Answer:
In order: 19, 25, 30, 31, 32, 35, 48, 51, 59; the 5th value is 32.
After replacement: 19, 30, 31, 32, 35, 48, 51, 52, 59; the 5th value is 35.

Question 8. The weights (in kg) of 15 students are 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.
Answer:
Order: 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45. The 8th value is 35 kg.
New order: 25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46; the 8th value is still 35 kg.

Question 9. Thirty children were asked about the number of hours they watched TV last week: 1, 6, 2, 3, 5, 12, 5, 8, 4, 8, 10, 3, 4, 12, 2, 8, 15, 1, 17, 6, 3, 2, 8, 5, 9, 6, 8, 7, 14, 12. (i) Make a grouped frequency table with class width 5 and one class 5-10. (ii) How many children watched for 15 or more hours?
Answer:
(i) Classes 0-5, 5-10, 10-15, 15-20 (lower limit included) have frequencies 10, 13, 5 and 2 (total 30).
(ii) The values 15 and 17 are 15 or more, so 2 children.

Question 10. The ages of ten students are 8 y 6 m, 9 y 0 m, 8 y 4 m, 9 y 3 m, 7 y 8 m, 8 y 11 m, 8 y 7 m, 9 y 2 m, 7 y 10 m, 8 y 8 m. Find the lowest age, the highest age and the range.
Answer:
Lowest age 7 y 8 m; highest age 9 y 3 m.
Range \( =9\text{ y }3\text{ m}-7\text{ y }8\text{ m}=1\text{ y }7\text{ m} \).