Understanding Data — NCERT Solutions

The appropriate statistical techniques are:

a) Compare performance in terms of division secured by students in Class XII A and Class XII B where each class strength is same

• Use Mean or percentage-based average to compare overall performance.
• Since both classes have the same strength, the average division level gives a fair comparison.

b) Five unit tests from July to November and want to compare class performance in these five months

• Use Mean for each month or test to compare the average performance across the five months.
• This helps in seeing which month had better or weaker class performance.

So, mean is the suitable technique in both cases because the teacher wants to compare average performance.

a) To find out the number of students whose both parents are alumni of the school, use counting/frequency on the relevant data.

b) To find how varied the ages of the parents are, use Range or Standard Deviation. Since the question asks about variation, standard deviation is a suitable measure of dispersion, and range also shows spread between the maximum and minimum ages.

a) The teacher should use structured data collection through an observation sheet / rating sheet so that the skills of students can be recorded systematically.

b) The skills can be represented as attributes/variables in a table, for example:

• Singing skill
• Writing skill
• Monitoring skill

Each student can be given ratings or scores for these skills, and the data can be stored in rows and columns.

Structured data is organized in a well-defined format, usually in rows and columns.

• Example: marks of students in a table, or a fee slip with fixed fields.

Unstructured data is not arranged in a traditional row-column format.

• Example: a newspaper article, email content, or a video file.

So, structured data is easy to store and process in tabular form, while unstructured data has no fixed pattern.

Create a dataset with purchase price, sale price, and items such as fruit juice, biscuits, and samosa. Then apply suitable statistical techniques:

Example dataset

For fruit juice and biscuits, compare purchase price and sale price directly.

• Fruit juice: profit = $25 - 18 = 7$
• Biscuits: profit = $15 - 10 = 5$

For sales of fruit juice, biscuits and samosa, compare their sale prices.

• Fruit juice sale price = 25
• Biscuits sale price = 15
• Samosa sale price = 12

For variation in sale price of fruit juices of different companies for same quantity, use Range or Standard Deviation.

• Range shows the difference between highest and lowest sale price.
• Standard deviation shows the spread of sale prices around the mean.

So, for comparison of prices, use the tabular dataset and basic techniques like difference, mean, and range/standard deviation.