To analyze the data provided in the given table of the masses of form one students at Mtakuja Secondary School, we will follow the steps below:
(i) Find the total number of students
To find the total number of students, we will sum the frequencies given:
- Frequency of 41-45 kg: 3
- Frequency of 46-50 kg: 8
- Frequency of 51-55 kg: 13
- Frequency of 56-60 kg: 11
- Frequency of 61-65 kg: 7
- Frequency of 66-70 kg: 3
Total Frequency (Number of Students): \[ 3 + 8 + 13 + 11 + 7 + 3 = 45 \]
Therefore, the total number of students is 45.
(ii) Draw frequency polygon and histogram on the same axes
Histogram
To draw a histogram, we will plot the frequency against the midpoints of the mass intervals.
First, we need to calculate the midpoints of each mass interval:
- For 41-45 kg: Midpoint = \( (41 + 45)/2 = 43 \)
- For 46-50 kg: Midpoint = \( (46 + 50)/2 = 48 \)
- For 51-55 kg: Midpoint = \( (51 + 55)/2 = 53 \)
- For 56-60 kg: Midpoint = \( (56 + 60)/2 = 58 \)
- For 61-65 kg: Midpoint = \( (61 + 65)/2 = 63 \)
- For 66-70 kg: Midpoint = \( (66 + 70)/2 = 68 \)
Next, we plot the frequencies:
- 43 kg: 3
- 48 kg: 8
- 53 kg: 13
- 58 kg: 11
- 63 kg: 7
- 68 kg: 3
The histogram bars will have widths corresponding to the mass intervals, and their heights will correspond to the frequencies.
Frequency Polygon
To draw the frequency polygon, we will plot the midpoints against the frequencies as points and then connect them with straight lines.
-
Plot the points:
- (43, 3)
- (48, 8)
- (53, 13)
- (58, 11)
- (63, 7)
- (68, 3)
-
Connect these points with straight lines.
Summary of Data for Plotting
| Mass Interval (kg) | Midpoint | Frequency | |-------------------|----------|-----------| | 41-45 | 43 | 3 | | 46-50 | 48 | 8 | | 51-55 | 53 | 13 | | 56-60 | 58 | 11 | | 61-65 | 63 | 7 | | 66-70 | 68 | 3 |
Graphing
While I cannot create visual plots directly, you can create the histogram and frequency polygon using graphing software or plotting by hand. Here are the steps:
- Draw the x-axis and y-axis: The x-axis will represent mass (kg) and the y-axis will represent frequency.
- Histogram Bars: For each mass interval, draw a rectangle (bar) when the mass is on the x-axis and the frequency is on the y-axis.
- Frequency Polygon: Plot the midpoints and frequencies, then connect them with lines.
Make sure to label your axes and include a key to differentiate between the histogram and frequency polygon if needed.
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