Mathematics
STATISTICS
STATISTICS
In this topic (Statistics), students will study how to collect, organize, present, analyze, and interpret data in meaningful ways.
Frequency tables
A frequency table is a way of organizing data to show how often each value or category appears. It is a simple method to summarize and display information in a clear and organized way.
Identify procedure of constructing frequency table
Identify procedure of constructing frequency table
This video introduces the concept of building a frequency table. using tally
Activity 50
Read the following information
- Collect the Data: Gather all the raw data you want to organize. Example: Ages of 12 students – 12, 13, 12, 14, 12, 13, 14, 15, 13, 12, 14
- Make a table with three columns with a data, tally and frequency
- Write a data set in first column
- Count a number of times each item representing in tally
- Write frequency in third column
- Write a total frequency in last row of the table
Draw frequency table
Draw frequency table
Samples of frequency table
Exercise 60
- 1. A fruit seller recorded the number of bananas sold each day: 5, 6, 5, 7, 6, 5, 8, 7, 6, 5. Construct a frequency table with tally marks.
- 2. The number of buses a student used in 10 days: 2, 1, 2, 3, 2, 1, 2, 3, 1, 2. Organize the data into a frequency table.
- 3. The number of hours students studied in the evening: 1, 2, 1, 3, 2, 2, 1, 4, 3, 2. Construct a frequency table using tally marks.
- 4. A person recorded how many cups of water they drank daily: 6, 7, 5, 6, 8, 7, 6, 5, 7, 6. Form a frequency table with tally marks.
- 5. Goals scored by a player in 10 matches: 0, 1, 2, 1, 3, 2, 1, 0, 2, 1. Construct a frequency table.
Interpret data from frequency table
Interpret data from frequency table
Interpretation of data from frequency table
| Fruit | Tally | Frequency |
| Mango | 5 | |
| Banana | 8 | |
| Apple | 3 | |
| Orange | 4 |
- The most popular fruit is Banana (highest frequency = 8).
- The least chosen fruit is Apple (lowest frequency = 3).
- Mango and Orange are in between, showing moderate preference.
Interpretation of data from frequency table
| Food | tally | Frequency |
| Rice | 12 | |
| Beans | 7 | |
| Meat | 10 | |
| Cassava | 6 | |
| Maize | 4 |
- The most popular food is rice (highest frequency = 12).
- The least popular food is maize (lowest frequency = 4).
- Meat is moderately preferred.
| Transport | Tally | Frequency |
| Car | 5 | |
| Bicycle | 10 | |
| Walking | 7 | |
| Bus | 19 |
- Interpretation: Most students go to school by Bus (frequency = 19). ·
- Least common mode is Car (frequency = 5). ·
- Bicycle and Walking are moderately common.
Exercise 61
Histogram
A histogram is a type of bar graph used in statistics to represent the frequency of data. It is usually used for continuous numerical data, such as marks, height, weight, or temperature.
- Key Features of a Histogram
- Bars are drawn adjacent to each other – no gaps between bars, unlike a regular bar chart.
- Width of each bar represents a class interval (range of values).
- Height of each bar represents the frequency of that class.
- It helps to visualize the distribution of data easily.
Identify the procedure of constructing histogram
Identify the procedure of constructing histogram
Procedure for Constructing a Histogram
Draw histogram
Draw histogram
Activity 51
Study the following: Construction of histogram
| Age interval | frequency |
| 20- 29 | 2 |
| 30-39 | 4 |
| 40-49 | 4 |
| 5059 | 5 |
| 60-69 | 3 |
| 70-79 | 1 |
| 80-89 | 0 |
| 90-99 | 1 |
| GPD | Frequency (Year) |
| 60-65 | 60 |
| 65-70 | 80 |
| 70-75 | 50 |
| 75-80 | 100 |
| 80-86 | 40 |
Exercise 62
Interpret data from the histogram
Interpret data from the histogram
Activity 52
Study the following examples and answer the following questions
Line graph
A line graph is a type of graph that uses points connected by straight lines to show how a variable changes over time or in relation to another variable
Identify concept of line graph
Identify concept of line graph
Activity 53
Observe the following informationA line graph is a type of graph that uses points connected by straight lines to show how a variable changes over time or in relation to another variable. It is particularly useful for showing trends, patterns, or changes.
Procedure for Constructing a Line Graph
Construct line graph
Construct line graph
Activity 54
Observe the following line grapgh
| Month | Viewing time (minutes) |
| January | 108 |
| February | 103 |
| March | 108 |
| April | 120 |
| May | 115 |
| June | 122 |
| July | 116 |
| August | `105 |
| September | 109 |
| October | 105 |
| November | 104 |
Exercise 63
Draw the line graph from the following data
| English scores | Frequency |
| 81-85 | 6 |
| 76-80 | 10 |
| 71-75 | 15 |
| 66-70 | 8 |
| 61-65 | 12 |
| Height (cm) | Frequency |
| 160 | 25 |
| 165 | 20 |
| 170 | 15 |
| 175 | 30 |
| 180 | 10 |
Analyze information from the line graph
Analyze information from the line graph
Activity 55
Study the following information
Maximum Sales: The highest sales volume was recorded in December (350 sales), likely due to seasonal demand or end-of-year promotions. Minimum Sales: The lowest sales volume occurred in January (120 sales). Fluctuations: While the general trend is positive, there were minor dips in March, June, and September. However, in each instance, the following month showed a strong recovery that surpassed the previous peak.
Exercise 64
Analyse the following line graphs
Pie chart
A
Identify the concept of pie chart
Identify the concept of pie chart
Activity 56
A pie chart is a circular chart divided into sectors (slices), where each sector represents a part of the whole. The size of each sector is proportional to the frequency, percentage, or fraction of that category. Pie charts are often used to show how a total is divided among categories.
Construct pie chart
Construct pie chart
Procedure to construct a pie chart
Example 53
Study the following example
Exercise 65
From each of the following data, draw pie chart and answer the questions
- Exercise 1: The table below shows the monthly household expenditure of a family in Zanzibar (in TZS):
| Category | Amount (TZS) |
| Food | 120,000 |
| Rent | 80,000 |
| Transport | 50,000 |
| School Fees | 30,000 |
| Healthcare | 20,000 |
- Exercise 2: Monthly income from different fishing activities:
| Activity | Income (TZS) |
| Tuna Fishing | 100,000 |
| Lobster Selling | 50,000 |
| Crab Selling | 30,000 |
| Day Tours | 20,000 |
- Exercise 3: Survey of 200 residents on their primary mode of transport:
| Transport Mode | Number of People |
| Daladala (Bus) | 80 |
| Boda-boda | 50 |
| Personal Car | 40 |
| Bicycle | 20 |
| Walking | 10 |
- Exercise 4: Survey of tourists’ preferred activities:
| Activity | Number of Tourists |
| Beach Visits | 150 |
| Spice Tour | 50 |
| Stone Town Tour | 70 |
| Diving | 30 |
- Exercise 5: Number of students in each club:
| Club | Number of Students |
| Football | 40 |
| Netball | 25 |
| Drama | 15 |
| Science Club | 20 |
| Art Club | 10 |
Interpret and solve word problems involving pie chart
Interpret and solve word problems involving pie chart
Exercise 66
Listening to this topic
