Statistics | Class 10 Mathematics Notes

Introduction

Statistics is a branch of mathematics that deals with the collection, organization, presentation, analysis, and interpretation of data. It helps us to make decisions based on data collected from various sources. In our daily life, we encounter data in different forms such as marks obtained by students, daily temperature, number of plants in a locality, etc. The process of statistics involves several steps: first, data collection from a population or sample; second, organizing the data in a meaningful way; third, presenting the data using tables, graphs, or charts; fourth, analyzing the data to find patterns or trends; and finally, interpreting the results to make informed decisions. This chapter focuses on the measures of central tendency, which summarize data by identifying a central or typical value. The three main measures of central tendency discussed are mean, median, and mode. These help us understand the average or most common values in the data set. Understanding these concepts is essential for analyzing data effectively in various fields such as education, economics, and social sciences.

📊 Diagram: Figure 1 on page 1; Figure 2 on page 1

🧪 Activity: Students are encouraged to collect data from their environment, such as daily temperatures or heights of classmates, and organize it to understand the process of statistics.

🔗 Connection: Leads to the next section on calculating the mean of ungrouped data, introducing the first measure of central tendency.

Table on page 8 (1×3)

| Percentage of female teachers | Number of States /U.T. ( f ) i | x i |

| 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 75 - 85 | 6 11 7 4 4 2 1 | 20 30 40 50 60 70 80 |

Table on page 11 (1×8)

Table on page 12 (4×13)

| | Number of heartbeats per minute | | 65 - 68 | 68 - 71 | 71 - 74 | | 74 - 77 | 77 - 80 | 80 - 83 | | 83 - 86 | |

| Number of women 2 4 3 8 7 4 2 5. In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Number of mangoes 50 - 52 53 - 55 56 - 58 59 - 61 62 - 64 Number of boxes 15 110 135 115 25 Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose? 6. The table below shows the daily expenditure on food of 25 households in a locality. Daily expenditure 100 - 150 150 - 200 200 - 250 250 - 300 300 - 350 (in `) Number of 4 5 12 2 2 households Find the mean daily expenditure on food by a suitable method. 7. To find out the concentration of SO in the air (in parts per million, i.e., ppm), the data 2 was collected for 30 localities in a certain city and is presented below: Concentration of SO (in ppm) Frequency 2 0.00 - 0.04 4 0.04 - 0.08 9 0.08 - 0.12 9 0.12 - 0.16 2 0.16 - 0.20 4 | Number of women | | 2 | 4 | 3 | | 8 | 7 | 4 | | 2 | | | | | Concentration of SO (in ppm) 2 | | | | Frequency | | | | | | | | | | 0.00 - 0.04 0.04 - 0.08 0.08 - 0.12 0.12 - 0.16 0.16 - 0.20 | | | | 4 9 9 2 4 | | | | | | |

Table on page 13 (5×18)

| | | Number of days | | 0 - 6 | | 6 - 10 | 10 - 14 | 14 - 20 | | 20 - 28 | | 28 - 38 | | 38 - 40 | | | |

| students 9. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate. Literacy rate (in %) 45 - 55 55 - 65 65 - 75 75 - 85 85 - 95 Number of cities 3 10 11 8 3 13.3 Mode of Grouped Data Recall from Class IX, a mode is that value among the observations which occurs most often, that is, the value of the observation having the maximum frequency. Further, we discussed finding the mode of ungrouped data. Here, we shall discuss ways of obtaining a mode of grouped data. It is possible that more than one value may have the same maximum frequency. In such situations, the data is said to be multimodal. Though grouped data can also be multimodal, we shall restrict ourselves to problems having a single mode only. Let us first recall how we found the mode for ungrouped data through the following example. Example 4 : The wickets taken by a bowler in 10 cricket matches are as follows: 2 6 4 5 0 2 1 3 2 3 Find the mode of the data. Solution : Let us form the frequency distribution table of the given data as follows: Number of 0 1 2 3 4 5 6 wickets | | students | | | | | | | | | | | | | | | | | | Number of wickets | | 0 | | 1 | | 2 | | 3 | | 4 | | 5 | | 6 | | |

| | Number of matches | | 1 | | 1 | | 3 | | 2 | | 1 | | 1 | | 1 | | |