Long Answer Questions: Statistics - 2

Class 10 Maths Chapter 13 Question Answers - Statistics

Q11. Find the mean, mode and median of the following data:

 Class Frequency 0-10 3 10-20 4 20-30 7 30-40 15 40-50 10 50-60 7 60-70 4

Sol. Let the assumed mean ‘a’ = 35

Here, h =10

 Classes xi fi cf fiui 0-10 5 3 3 + 0 = 3 -3 (-3) x 3 = -9 10-20 15 4 4 + 3 = 7 -2 (-2) x 4 = -8 20-30 25 7 7 + 7 = 14 -1 (-1) x 7 = -7 30-40 35 15 15 + 14 = 29 0 0 x 15 = 0 40-50 45 10 10 + 29 = 39 1 1 x 10 = 10 50-60 55 7 7 + 39 = 46 2 2 x 7 = 14 60-70 65 4 4 + 46 = 50 3 3 x 4 = 12 Total ∑fi = 50 ∑uifi = 12

(i)

(ii) To find mode
Here, greatest frequency = 15
∴ Modal class = 30 − 40
l = 30, f1 = 15, f0 = 7, f2 = 10 and h = 10

So,
⇒

(iii) To find median

Here,
∴ Median class is 30−40.
Such that l = 30, cf = 14, f = 15 and h = 10

Q12. The following table gives daily income of 50 workers of a factory:

 Daily income (in Rs) 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10

Find the mean, mode and median of the above data.

Sol. Let assumed mean a = 150. Here, h = 20

 Daily income (in Rs) No. of workers (fi) xi fi ui cf 100-120 12 110 -2 -24 12 + 0 = 12 120-140 14 130 -1 -14 12 + 14 = 26 140-160 8 150 0 0 26 + 8 = 34 160-180 6 170 1 6 34 + 6 = 40 180-200 10 190 2 20 40 + 10 = 50 Total ∑ fi = 50 ∑ fiui  =-12

(i) Mean

Thus, mean income is Rs 145.2

(ii) For finding the mode,
We have the greatest frequency = 14 which lies in the class 120−140
∴ Modal class = 120−140
Therefore, l = 120
f1 = 14
f0 = 12
f2 = 8
and h = 20

(iii) For finding median,

And 25 lies in the class 120−140

Median class is 120−140

Since n/2 = 25, cf = 12, f = 14 and h = 20

Median income = Rs138.57

Q13. Find the mode, median and mean for the following data:

 Marks obtained 25-35 35-45 45-55 55-65 65-75 75-85 Number of students 7 31 33 17 11 1

Sol. Let the assumed mean a = 60. Here h = 10, we have:

 Marksobtained Class marksxi fi cf fi ui 25-35 30 7 7 -3 -21 35-45 40 31 38 -2 -62 45-55 50 33 71 -1 -33 55-65 60 17 88 0 0 65-75 70 11 99 1 11 75-85 80 1 100 2 2 Total ∑ f = 100 ⇒ n = 100 ∑ fiui =-103

(i)
⇒
(ii) Median

Here,

∴ Median class is 45−55.

l = 45
cf = 38
f = 33 and h = 10

(iii) Mode: Greatest frequency is 33 which corresponds to the class 45−55.

l = 45,  h = 10
f1 = 33,  f2 = 17
f0 = 31

Q14. A survey regarding the heights (in cm) of 50 girls of Class X of a school was conducted and the following data was obtained:

 Height (in cm) 120-130 130-140 140-150 150-160 160-170 Total Number of girls 2 8 12 20 8 50

Find the mean, median and mode of the above data.

Sol. We have:

 Height (in cm) f cf xi fixi 120-130 2 2 + 0 = 2 125 250 130-140 8 2 + 8 = 10 135 1080 140-150 12 10 + 12 = 22 145 1740 150-160 20 22 + 20 = 42 155 3100 160-170 8 42 + 8 = 50 165 1320 Total 50 7490

(i)

(ii) ∵

∴ Median class is 150−160.
∴ We have,
l = 150
f = 20
cf = 2
2h = 10

∴
⇒

(iii) ∵ Greatest frequency = 20
∴ Modal class = 150−160

So, we have

l = 150, f0 = 12, f1 = 20
f2 = 8 and h = 10

Q15. Find the mean, mode and median of the following data:

 Classes Frequency 0-10 5 10-20 10 20-30 18 30-40 30 40-50 20 50-60 12 60-70 5

Sol.

(i) Mean:

Let the assumed mean ‘a’ = 35

Now we have the following data:

 Class Class mark xi fi Cf fiui 0-10 5 5 5 + 0 = 5 -3 (-3) x 5 = -15 10-20 15 10 5 + 10 = 15 -2 (-2) x 10 = -20 20-30 25 18 15 + 18 = 33 -1 (-1) x 18 = -18 30-40 35 30 33 + 30 = 63 0 0 x 30 = 0 40-50 45 20 63 + 20 = 93 1 1 x 20 = 20 50-60 55 12 83 + 12 = 95 2 2 x 12 = 24 60-70 65 5 95 + 5 = 100 3 3 x 5 = 15

Here ∑fi = 100 and ∑fiui = 6

(ii) Mode:

Here, the maximum frequency is 30.
∴ Modal class is 30−40.
So, we have

l = 30, h = 10
f1 = 30,
f0 = 18
f2 = 20

(iii) Median:

∴ Median class = 30−40
So, we have:

l = 30, h = 10, cf = 33, f = 30

Q16. Find the mean, mode and median for the following data:

 Classes Frequency 0-10 3 10-20 8 20-30 10 30-40 15 40-50 7 50-60 4 60-70 3

Sol. Let the assumed mean = 35;  h = 10

 Classes xi fi cf fiui 0-10 5 3 3 + 0 = 3 -3 (-3) x 3 = -9 10-20 15 8 3 + 8 = 11 -2 (-2) x 8 = -16 20-30 25 10 11 + 10 = 21 -1 (-1) x 10 = -10 30-40 35 15 21 + 15 = 36 0 0 x 15 = 0 40-50 45 7 36 + 7 = 43 1 1 x 7= 7 50-60 55 4 43 + 4 = 47 2 2 x 4= 8 60-70 65 3 47 + 3 = 50 3 3 x 3= 9 Total ∑fi = 50 ∑fiui= -11

Now,

(i)

(ii) To find mode
Here, highest frequency is 15.
∴ Modal class is 30−40.

Here,

l = 30, f1 = 15, f0 = 10
f2 = 7 and h = 10

(iii) ∵

So, the median class is 30−40.

∴ We have l = 30, cf = 21, f = 15 and h = 10

We have

The document Class 10 Maths Chapter 13 Question Answers - Statistics is a part of the Class 10 Course Mathematics (Maths) Class 10.
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Mathematics (Maths) Class 10

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FAQs on Class 10 Maths Chapter 13 Question Answers - Statistics

 1. What is statistics and why is it important in the field of data analysis?
Ans. Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides a framework for making informed decisions and drawing conclusions from data. In the field of data analysis, statistics helps in summarizing and describing data, identifying patterns and relationships, making predictions, and testing hypotheses. It plays a crucial role in various disciplines such as economics, business, medicine, social sciences, and many others.
 2. What are the different types of data in statistics?
Ans. In statistics, data can be classified into four main types: categorical, ordinal, interval, and ratio. Categorical data represents different categories or groups and cannot be ordered or measured numerically. Ordinal data has a natural order but the differences between the values are not meaningful. Interval data represents values with meaningful differences but does not have a true zero point. Ratio data has a true zero point and meaningful differences between values. Understanding the type of data is important as it determines the appropriate statistical techniques and methods to be used for analysis.
 3. How is the mean calculated in statistics?
Ans. The mean is a measure of central tendency that represents the average value of a dataset. To calculate the mean, the sum of all the values in the dataset is divided by the total number of values. Mathematically, it can be represented as: Mean = (Sum of all values) / (Total number of values) For example, to find the mean of the dataset {5, 8, 10, 12, 15}, we add all the values (5 + 8 + 10 + 12 + 15 = 50) and divide it by the total number of values (5). Therefore, the mean is 50/5 = 10.
 4. What is the difference between correlation and regression in statistics?
Ans. Correlation and regression are both statistical techniques used to analyze the relationship between variables. However, they differ in their purpose and approach. Correlation measures the strength and direction of a linear relationship between two variables. It quantifies how closely the variables are related, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation). Regression, on the other hand, is used to model and predict the relationship between variables. It aims to find the best-fitting line (regression line) that minimizes the difference between the observed and predicted values. Regression also allows us to estimate the effect of one variable on another and make predictions based on the relationship.
 5. What is the significance of hypothesis testing in statistics?
Ans. Hypothesis testing is a statistical method used to make inferences about a population based on a sample. It involves formulating a hypothesis, collecting data, and analyzing it to determine if the evidence supports or contradicts the hypothesis. The significance of hypothesis testing lies in its ability to provide statistical evidence for or against a claim or theory. It helps researchers and analysts make objective decisions, identify patterns or relationships in the data, and draw conclusions about the population. Hypothesis testing also allows for the evaluation of the effectiveness of interventions or treatments and is widely used in scientific research and decision-making processes.

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