NCERT Solutions Ganita Prakash (Part 2) Chapter 5 –123Section 5.2 Visualising and Interpreting Data — Figure it Out
Book page 122 Updated on2026-09-05
Q1.
The average number of customers visiting a shop and the average number of customers actually purchasing items over different days of the week is shown in the table below. Visualise this data on a line graph.
Answer
Day
Mon
Tue
Wed
Thu
Fri
Sat
Sun
Visiting
16
19
10
14
20
22
35
Purchasing
10
8
7
11
12
16
26
Put the days along the horizontal axis and the number of customers up the vertical axis. A scale of 1 cm to 5 customers, running from 0 to 35, holds every value comfortably. Plot both series on the same axes and use different marks so the two can be told apart even in black and white.
Customers visiting and purchasing at the shop across the week. Both lines dip on Wednesday and climb steeply into Sunday.
What the graph says: both lines rise towards the weekend and peak sharply on Sunday. Wednesday is the quietest day. The gap between the lines is the number who look but do not buy — widest on Tuesday (19 visiting, only 8 purchasing) and narrowest on Monday and Thursday.
Q2.
The average number of days of rainfall in each month for a few cities is shown in the table below: (i) What could be the possible method to compile this data? (ii) Mark the data for Mangaluru, Port Blair, and Rameswaram in the line graph shown below. You can round off the values to the nearest integer. (iii) Based on the line for New Delhi in the graph fill the data in the table. (iv) Which city among these receives the most number of days of rainfall per year? Which city gets the least number of days of rainfall per year? (v) Looking at the table, when is the rainy season in New Delhi and Rameswaram?
Answer
(i) For each city, note on how many days of a given month rain was recorded at the weather station. Do this for several years, then average the counts for that month. So ‘24.1 days in June at Mangaluru’ means that on average it rained on about 24 days of June. That is why the figures come with decimals — no single June has 24.1 rainy days.
(ii) Round each figure to the nearest whole number and plot the points, joining each city’s points with its own line:
City
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Mangaluru
0
0
0
2
6
24
28
25
14
9
4
1
Port Blair
2
1
1
3
16
19
17
19
17
14
11
5
Rameswaram
3
1
2
3
3
0
1
1
2
8
10
8
The vertical scale of the printed graph runs from 0 to 30, so every rounded value fits.
(iii) Reading the New Delhi line off the graph, month by month:
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
New Delhi
1
2
2
1
2
4
10
10
4
1
0
1
Read to the nearest whole number, as the question allows. Reading a graph is never exact — a classmate might read July as 9 or 10, and either is a fair reading of the printed line.
Port Blair gets the most rainy days (about 126 a year) and New Delhi the fewest (about 38).
Worth noticing: Mangaluru has fewer rainy days than Port Blair yet is far wetter overall — its rain arrives in three furious months. ‘Number of rainy days’ and ‘amount of rain’ are different measurements, and this table only records the first.
(v) New Delhi’s rainy season is July and August, with the build-up in June and the tail in September — the south-west monsoon. Rameswaram’s rainy season is October to December, with November the wettest — the north-east monsoon. The two cities get their rain at almost opposite times of the year.
Q3.
The following line graph shows the number of births in every month in India over a time period: (i) What are your observations? (ii) What was the approximate number of births in July 2017? (iii) What time period does the graph capture? (iv) Compare the number of births in the month of January in the years 2018, 2019, and 2020. (v) Estimate the number of births in the year 2019.
Answer
(The book prints this question as ‘2’ again; it is the third question of this set.)
(i) Observations. The line never falls below about 1.4 million or rises above about 2 million, so births each month stay in a fairly narrow band. Inside that band there is a clear repeating yearly pattern: a peak around August–October every year and a dip around February and April. The pattern repeats three times, once for each year on the graph, and the whole band drifts very slightly upwards over the three years.
(ii) Reading the point above July 2017: about 1.75 million births (roughly 17.5 lakh).
(iii) The first point sits about three months before the July 2017 gridline and the last about three months after January 2020, so the graph runs from about April 2017 to March 2020 — three years, 36 monthly points.
(iv) Reading the three January points:
Month
Approximate births
January 2018
about 1.68 million
January 2019
about 1.76 million
January 2020
about 1.77 million
January births rose noticeably from 2018 to 2019 and then stayed almost level in 2020. All three are close to one another, and all three are well below that year’s autumn peak — January is a middling month for births, not a low one.
Quicker estimate: the 2019 points hover around 1.8 million a month, and 12 × 1.8 = 21.6 million — close to the careful total. When every value in a graph sits near one level, multiplying that level by the number of points is a good estimate, and it is a use of the mean in reverse.