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QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis

Analyze bivariate data on median household income and percentage of mortgage-paying homeowners spending over 30% on housing costs in eight Ghanaian regions, explain bivariate data, draw scatter diagram and line, comment on relationship, calculate least squares line, and compare lines.

Nationwide, about 27% of mortgage-paying home owners spent 30% or more of their income on
housing costs. Upper East region residents paid the largest percentage at 41% and the Greater
Accra residents the smallest at 17.5%. Eight regions were randomly selected, and the median
household income(X) in thousands and percentage of mortgage -paying homeowners whose housing
costs exceed 30 % of their income (Y) are as follows:

Regions Greater
Accra

Upper East

Bono
East

Ashanti Volta
Eastern Western Savannah

X 46.5 51.1 37.1 36.4 33.5 35.2 45.6 28.6 Y 37.2 41.0 20.6 24.3 22.0 17.5 30.0 23.0

(a) Briefly explain the term (X,Y) is bivariate data                                                                                                                                                  (b) Draw

(i) Scatter diagram for the data above (ii) a line through the points (c) Using (b) comment on the relationship between X and Y.  (d) Calculate the least square line (e) Comment on the lines in (b)-(ii) and (d) above.

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QMDM – APR 2023 – L2 – Q1 – Frequency Distribution and Charts for Patient Heights

Explain differences in charts, construct frequency table and charts for heights of 40 patients.

Central Legon Hospital in Accra recorded the Height (in cm) of 40 patients reporting to the OPD in a day and come up with the following figures:

150 141 158 147 132 153 176 162 180 165 174 133 129 119 133 188 190 165 157 146 161 130 122 169 159 152 173 148 154 171 136 155 141 153 147 168 150 140 161 185

(a) Explain (briefly) the difference between a percentage frequency bar chart and cumulative percentage frequency bar graph for the height of the 40 patients to the director of the Central Legon Hospital. [5 Marks]

(b) Using classes 110 – 119,120 – 129,130 – 139 and so on, construct a frequency distribution table for the heights of the 40 patients. [10 Marks]

(c) Using (b) above, a percentage frequency bar chart and a cumulative percentage frequency bar chart on the same graph. i.e. super – impose the cumulative percentage frequency chart on percentage frequency bar chart. [8 Marks]

(d) Comment on your charts in (c) above. [2 Marks]

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QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis

Analyze bivariate data on median household income and percentage of mortgage-paying homeowners spending over 30% on housing costs in eight Ghanaian regions, explain bivariate data, draw scatter diagram and line, comment on relationship, calculate least squares line, and compare lines.

Nationwide, about 27% of mortgage-paying home owners spent 30% or more of their income on
housing costs. Upper East region residents paid the largest percentage at 41% and the Greater
Accra residents the smallest at 17.5%. Eight regions were randomly selected, and the median
household income(X) in thousands and percentage of mortgage -paying homeowners whose housing
costs exceed 30 % of their income (Y) are as follows:

Regions Greater
Accra

Upper East

Bono
East

Ashanti Volta
Eastern Western Savannah

X 46.5 51.1 37.1 36.4 33.5 35.2 45.6 28.6 Y 37.2 41.0 20.6 24.3 22.0 17.5 30.0 23.0

(a) Briefly explain the term (X,Y) is bivariate data                                                                                                                                                  (b) Draw

(i) Scatter diagram for the data above (ii) a line through the points (c) Using (b) comment on the relationship between X and Y.  (d) Calculate the least square line (e) Comment on the lines in (b)-(ii) and (d) above.

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QMDM – APR 2023 – L2 – Q1 – Frequency Distribution and Charts for Patient Heights

Explain differences in charts, construct frequency table and charts for heights of 40 patients.

Central Legon Hospital in Accra recorded the Height (in cm) of 40 patients reporting to the OPD in a day and come up with the following figures:

150 141 158 147 132 153 176 162 180 165 174 133 129 119 133 188 190 165 157 146 161 130 122 169 159 152 173 148 154 171 136 155 141 153 147 168 150 140 161 185

(a) Explain (briefly) the difference between a percentage frequency bar chart and cumulative percentage frequency bar graph for the height of the 40 patients to the director of the Central Legon Hospital. [5 Marks]

(b) Using classes 110 – 119,120 – 129,130 – 139 and so on, construct a frequency distribution table for the heights of the 40 patients. [10 Marks]

(c) Using (b) above, a percentage frequency bar chart and a cumulative percentage frequency bar chart on the same graph. i.e. super – impose the cumulative percentage frequency chart on percentage frequency bar chart. [8 Marks]

(d) Comment on your charts in (c) above. [2 Marks]

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