Statistics questions | form three Basic Mathematics

In a mathematics test the following marks were obtained:
27, 57, 57, 40, 70, 48, 59, 60, 42, 44, 47, 44, 44, 59, 35, 48, 43, 52, 36, 48
(a) Group the marks in class intervals 20 – 29, 30 – 39, etc. and then construct the
frequency distribution table.
(b) Draw the histogram for the distribution.

Carefully study the frequency distribution table which shows the marks of 100 students in a Physics examination.

Calculate
(a) the mean given the assumed mean is 75.5,
(b) the median in two decimal places,
(c) the mode in two decimal places.

Mode , median and mean are the measures of central tendency of a distribution. Give a description of each term.

The following frequency distribution table shows the marks of 100 students in an end of term Mathematics examination.

1. How many students had less than 71 marks?
2. How many students had at least 41 marks?
3. Determin the modal and the median classes.
4. Determine an estimate mean of the marks.
5. Draw a cumulative frequency curve of the marks.
6. Estimate the median examination mark from the graph.

The following distribution table shows the scores of 64 students in a Chemistry weekly test.

1. Calculate the mean and mode.
2. Draw the ogive and use it to estimate the median.

The information on age of employees of certain organization is given in the frequency table below.

1. Draw on the same axes to represent the given information :

1. a histogram
2. a frequency polygon

2. Calculate the mean, mode and median.
3. Comment on the results in part (a) and (b) above.

The following data represent the marks scored by 36 students of a certain school in Geography examination:

1. Prepare a frequency distribution table representing the given data by using the class interval: 50-54, 55-59, 60-64, and so on.
2. Use the frequency distribution table obtained in part(a) to:

1. Draw a histogram.
2. Calculate the median. Write the answer correct to 2 decimal places.

The following marks were obtained by 32 students in a physics examination:

32, 35, 42, 50, 46, 29, 39, 38, 45, 37, 48, 52, 37, 58, 52, 48, 36, 54, 37, 42, 64, 37, 34, 28, 58, 64, 34, 57, 54, 62, 48, 67.

1. Prepare a frequency distribution table using the class intervals: 24-29, 30-35 etc.
2. Draw the histogram.
3. Draw the cumulative frequency curve and use it to estimate the median.
4. Find the mean mark.

The number of patients who attended maternity clinic daily in June 2017 in a certain village was recorded as follows:

1. Make a frequency distribution by grouping the number of patients in the class intervals: 20-29, 30-39, 40-49,….
2. By using the frequency distribution table obtained in part (a), calculate the mean number of patients per day.
3. Construct a pie chart for the frequency ditribution obtained in part (a).

The scores of 45 pupils in a Civics test were recorded as follows:

1. Construct a frequency distribution table of the given data, taking equal class intervals: 21-40, 41-60…
2. Calculate the mean score.
3. Draw the cumulative frequency curve and use it to estimate the median.