Class 9 Maths Chapter 13 HOTS Questions - Statistics

Q1: Find the missing frequencies in the following frequency distribution. If it is known that the mean of the distribution is 50.16 and the total number of items is 125.
Sol:
Since total number of items = 125
∴ 17 + f₁ + 32 + f₁ + 19 = 125
f₁ + f₂ = 125 – 17 – 32 – 19
f₁ + f₂ = 57 …..(i)
Now, mean of data = 50.16
We know that

     .......(ii)
Multiplying (i) by 3, we have
3f₁ + 3f₂ = 171 ......(iii)
Substracting (iii) from (ii) we have


 = 27
Now put f₂ = 27 in (i), we have

f₁ = 57 - 27
Hence, f₁ = 30 and f₂ = 27

Q2:The mean weight of 60 students of a class is 52.75 kg. If mean weight of 25 students of this class is 51 kg, find the mean weight of remaining 35 students of the class.
Sol:
Total weight of 60 students = 60 × 52.75 kg = 3165 kg
Total weight of 25 students = 25 × 51 kg = 1275 kg
∴ Total weight of 35 students = (3165 – 1275) kg = 1890 kg
∴ Mean weight of 35 students = 1890 / 35 = 54 kg

Q3: Shimpi, a class IX student received cash award of 10000 (Ten thousand) in the singing competition. Her father advised her to make a budget plan for spending this amount. She made the following plan :
Make a bar graph for the above data.
From above answer the following questions :
(i) Which mathematical concepts have been covered in this ?
(ii) How will you rate her budget plan ? In your opinion which head has been given
(a) more than deserved and (b) less than it deserved ?
(iii) Which values are depicted in her plan?
Sol:
The bar graph of given data is given below :
In the graph, head is taken on X-axis and amount is taken on Y-axis.
(i) Representation of data using bar graph.
(ii) Very good
(a) Picnic for family
(b) Tuition fee for needy child
(iii) Help the needy people and respect the elders.

Q4: The following data on the number of girls (to the nearest ten) per thousand boys in different sections of the Indian society is given below :
(i) Represent the information above by a bar graph.
(ii) In the classroom, discuss what conclusions can be arrived at from the graph.
(iii) What steps should be taken to improve the situation ?
Sol:
(i) The required graph is given below :
In the graph, different sections of the society is taken on X-axis and number of girls per thousand boys is taken on the Y-axis.
[Scale : 1 cm = 10 girls.]
(ii) From the graph, the number of girls to the nearest ten per thousand boys are maximum in scheduled tribes whereas they are minimum in urban.
(iii) Pre-natal sex determination should strictly banned in urban.