CBSE Class 8 Mathematics Data Handling Notes Set 05

Organising Data

Data collected by observation or experiment is called raw data. To read it easily we arrange it in a frequency distribution table using tally marks. The frequency of an entry is the number of times it occurs.
When the data is large, we group it into classes such as 0-10, 10-20 and so on. This is a grouped frequency distribution. A value equal to the upper limit of a class is counted in the next class.

Class Intervals

Lower limit and upper limit: the smallest and largest values that mark the two ends of a class.
Class width (size) = upper limit - lower limit.
Class mark = (upper limit + lower limit) / 2. For the class 112.7 - 119.9 the class mark is 116.3.
Range of the distribution = upper limit of the last class - lower limit of the first class.

Graphs for Data

Pictograph: uses symbols, each standing for a fixed number of items.
Bar graph: bars of equal width and equal gaps; the height shows the quantity.
Double bar graph: two bars side by side for each category, used to compare two sets of data.
Histogram: bars with no gaps, one for each class interval; the height gives the frequency.

Pie Chart (Circle Graph)

A pie chart shows data as sectors of a circle. Each sector has a central angle, and the angles add up to 360 degrees.
Central angle = (value / total) x 360 degrees. To read a pie chart: value = (angle / 360) x total.

Worked example: a day of 24 hours is spent as sleep 8, school 7, games 2, homework 3, others 4 hours. One hour corresponds to 360/24 = 15 degrees, so the angles are 120, 105, 30, 45 and 60 degrees (total 360).

Chance and Probability

A random experiment has several possible outcomes and we cannot say in advance which one will occur (tossing a coin, throwing a die). The set of all outcomes is the sample space: for a coin {H, T}, for a die {1, 2, 3, 4, 5, 6}. Outcomes are equally likely if each has the same chance.
An event is one outcome or a collection of outcomes. P(A) = number of favourable outcomes / total number of outcomes, and P(not A) = 1 - P(A), so P(A) + P(not A) = 1.

Worked example: a bag has 4 red and 2 yellow balls. P(red) = 4/6 = 2/3 and P(yellow) = 2/6 = 1/3, so a red ball is more likely.

Quick Checks

Probability lies between 0 (impossible event) and 1 (certain event). For two coins the sample space is {HH, HT, TH, TT}; for two dice there are 36 equally likely outcomes.