The data below represent heights, measured in centimetres, of women from an adult female population: 162 164 164 165 165 166 166 166 167 167 167 167 167 168 168 168 168 168 168 169 169 169 169 170 170 170 171 172 184 185 (i)Carefully construct, draw and label a histogram of these data. (ii)Find the median height among these women and the upper quartile. What percentage of women were below 165 cm? (iii)Comment on the data given the shape of the histogram without doing any further calculations. (iv)Name two other types of graphical displays that would be suitable to represent the data.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The data below represent heights, measured in centimetres, of women from an adult female population:
162 164 164 165 165 166 166 166 167 167 167 167 167 168
168 168 168 168 168 169 169 169 169 170 170 170 171 172
184 185
(i)Carefully construct, draw and label a histogram of these data.
(ii)Find the
(iii)Comment on the data given the shape of the histogram without doing any further calculations.
(iv)Name two other types of graphical displays that would be suitable to represent the data.
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