Statistics- 1 - Free MCQ Practice Test with solutions, Class 9 Maths

The data collected by the student falls under the category of primary data. This type of data is defined as information gathered directly from the source, which in this case involves the number of school-going children from households in a specific locality.

• Primary data is original and collected for a specific purpose.
• It provides a firsthand account, ensuring accuracy and relevance.
• This contrasts with secondary data, which is obtained from existing sources.
• Examples of secondary data include statistics from previous studies or reports.

In summary, since the student personally gathered the information, it is classified as primary data.

The x-axis is one of the sides of a frequency polygon. The x-axis represents the values of the variable being measured.

To analyse election results, the data collected from newspapers is classified as:

• Secondary data: This refers to information that has been gathered by others, such as newspapers or reports. It is not collected firsthand by the researcher.

• Raw data: This is unprocessed information that has not yet been analysed or interpreted.

• Grouped data: This involves organising raw data into categories for easier analysis.

• Primary data: This is data collected directly by the researcher for a specific purpose.

In this context, the correct classification for the data collected from newspapers is secondary data.

class mark of 1st interval=212

class mark of 2nd interval=236.5

Step-by-step explanation:

First Class interval=200-224

class mark=upper limit +lower limit divided by 2..

class mark of first interval is =200+224 divided by 2=212

Second class interval=224-249

class mark of second interval =224 +249 divided by 2

answer= 236.5

Common Measures of Central Tendency are statistical values that represent a typical data point within a dataset. The main measures include:

• Mean: The average value, calculated by adding all numbers and dividing by the total count.
• Median: The middle value in a dataset when arranged in ascending or descending order.
• Mode: The value that occurs most frequently in a dataset.

However, the range is not considered a measure of central tendency. Instead, it indicates the spread or dispersion of data by subtracting the smallest value from the largest.

If the mean of x and 1/2 is M. then the mean of

x² and 1/x² is

Mean of x and 1/x is M. So

( x +1/x)/2=M

Squaring on both sides,

(x +1/x)²/2²=M²

(x² + 1/x²+2*x*1/x)/4=M²

x²+1/x²+2=4 m²

x²+ 1/x²=4m²-2

Dividing by 2 on both sides,

(x²+1/x²)/2=(4m²-2)/2

= (x²+1/x²)/2 =2 *(2m²-1)/2=2m²-1

=Mean of x² and 1/x²=(2m²-1)

Mode is the value that appears most frequently in a set of observations. It is an important measure in statistics as it helps identify the most common value within a dataset.

Key points about mode:

• The mode is not necessarily unique; a dataset can have more than one mode if multiple values occur with the same highest frequency.
• In cases where no number repeats, the dataset is said to have no mode.
• The mode is particularly useful for categorical data where we wish to know which is the most common category.

Unlike other measures of central tendency, such as the mean or median, the mode can be used for both numerical and non-numerical data. This makes it a versatile tool in data analysis.

Range is the term used to describe the difference between the highest and lowest values in a set of observations. It is a fundamental concept in statistics and is useful for understanding data variability. Here are some key points about range:

• The maximum observation is the largest value in the dataset.
• The minimum observation is the smallest value in the dataset.
• The range is calculated by subtracting the minimum observation from the maximum observation:
• Range = Maximum - Minimum
• It provides a quick measure of how spread out the values are.
• A larger range indicates greater variability, while a smaller range suggests that the data points are closer together.

Understanding the range helps in analysing data distributions and is a foundational aspect of statistics.

Let x and y be the upper and lower class limit of frequency distribution.
Given, width of the class = 5
⇒ x-y= 5 …(i)
Also, given lower class (y) = 10 On putting y = 10 in Eq. (i), we get
x – 10= 5 ⇒  x = 15 So, the upper class limit of the lowest class is 15.
Hence, the upper class limit of the highest class
=(Number of continuous classes x Class width + Lower class limit of the lowest class)
= 5 x 5+10 = 25+10=35
Hence,’the upper class limit of the highest class is 35.
Alternate Method
After finding the upper class limit of the lowest class, the five continuous classes in a frequency distribution with width 5 are 10-15,15-20, 20-25, 25-30 and 30-35.
Thus, the highest class is 30-35,
Hence, the upper limit of this class is 35.

The mean of the first four prime numbers can be calculated by following these steps:

• The first four prime numbers are 2, 3, 5, and 7.
• To find the mean, sum these numbers:
• 2 + 3 + 5 + 7 = 17
• Next, divide the total by the number of prime numbers:
• Mean = 17 ÷ 4 = 4.25

Therefore, the mean of the first four prime numbers is 4.25.

⇒  It is given that Mean of 5 observations is 15.

∴  The sum of observations =15×5=75.

∴  It is given that mean of the first 3 observations is 14.

∴  The sum of first three observations =14×3=42.

⇒  Given that mean of the last 3 observations is 17.

∴  The sum of the last three observations =17×3=51

∴  The third observation =(42+51)−75
 =93−75

=18