44. FICO Scores The Fair Isaacs Corporation has devised a...

44. FICO Scores The Fair Isaacs Corporation has devised a model that is used to determine creditworthiness of individuals, called a FICO score. FICO scores range in value from 300 to 850 with a higher score indicating a more credit-worthy individual. The distribution of FICO scores is skewed left with a median score of 723. (a) Do you think the mean FICO score is greater than, less than, or equal to $723 ?$ Justify your response. (b) What proportion of individuals have a FICO score above $723 ?$

44. FICO Scores The Fair Isaacs Corporation has devised a model that is used to determine creditworthiness of individuals, called a FICO score. FICO scores range in value from 300 to 850 with a higher score indicating a more credit-worthy individual. The distribution of FICO scores is skewed left with a median score of 723.
(a) Do you think the mean FICO score is greater than, less than, or equal to $723 ?$ Justify your response.
(b) What proportion of individuals have a FICO score above $723 ?$

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Key Concepts

Skewness of Distribution

Skewness refers to the asymmetry in the distribution of data. A left-skewed (negative skewed) distribution has a longer or fatter tail on the left side, meaning that a relatively small number of lower values pull the mean down. This characteristic is important in understanding how measures of central tendency, such as the mean, are affected, as they do not lie at the center of the distribution in skewed distributions.

Measures of Central Tendency

The mean is the arithmetic average, and the median is the middle value that divides the dataset into two equal parts. In a skewed distribution, particularly a left-skewed one, the mean is generally smaller than the median because the lower extreme values have a greater impact on the calculation of the mean, whereas the median is robust to such extreme values and always splits the data into halves.

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