Mathematical Techniques - Descriptive Statistics

​​Using appropriate formular, differentiate between “variance” and “standard deviation” as used in statistics.

​ ​ ​ ​ ​​The amount of sales in millions of shillings for 92 companies in the construction industry was recorded as shown below:

​​Highlight FOUR characteristics of arithmetic mean.

​ ​ ​ ​ ​ ​​A company collected data on monthly sales (in units) of a particular product over the past 100 months. The data was grouped into eight classes as shown below but two frequency values (​\(F_3\)​ and ​\(F_6\)​) are missing. The mean sale is given as 48.3 units.

​​Highlight SIX qualities of a good measure of central tendency.

​​State FOUR characteristics of the mean as a measure of central tendancy.

​ ​ ​ ​ ​​The following frequency distribution table shows the amount of annual electricity bill obtained from a local utility company’s annual report:

​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​​The amount of money spent on purchases by the first 50 customers at a large department store is summarised in the following table:

​​Highlight FOUR disadvantages of the mode as a measure of central tendency

​ ​ ​ ​ ​​The following data relates to the ages of 100 students attending a workshop on personal branding organised by the student welfare officials of Pride Business College:

​​With the aid of diagrams, describe the THREE types of Kurtosis.

​​Differentiate between the following terms:

​ ​ ​ ​​The time taken to complete a particular task was measured for 250 workers and the results were as shown below:

​ ​ ​ ​ ​​The following data relate to the number of computers sold each day over the last 240 working days by a leading computer firm.

​ ​ ​ ​ ​​The following data shows the distribution of profits of 150 manufacturing companies in a given year:

​ ​​Mwangaza Limited deals in the production of electric bulbs. A random sample of 10 electric bulbs produced by the company yielded the following results on the lifetime of the bulbs:

​​Apex Limited is planning to launch a new product in the market. It has undertaken a survey on the product's colour. brand name and packaging. The company sent questionnaires to 200 potential customers to obtain their views on the three attributes of the product. The results were as follows:

• 24 persons liked the packaging and the brand name.
• 77 persons liked the brand name or the colour but did not like the packaging.
• 40 persons liked the colour only.
• 120 persons liked the colour or the brand name.
• 23 persons liked the colour and the packaging.
• 43 persons liked at least two of the three attributes.
• 5 persons did not like any of the three attributes.
• The questionnaires of 25 persons were not received back.

The company's policy is to incorporate an attribute in the product if at least 50 per cent of the respondents liked the attribute.

Required:
(i) Present the above information in a venn diagram.

(ii) Number of persons that liked all the three attributes.

(iii) Proportion of persons that liked the colour.

(iv) Proportion of persons that liked the brand name.

(v) Proportion of persons that liked the packaging.

(vi) Attribute(s) to be incorporated in the product.