Final answer:
To compute the statistics requested, data must be ordered and calculations for mean, median, mode, range, interquartile range, variance, and standard deviation must be made either manually or via software such as Excel or SPSS. These statistics provide key insights into the dispersion and central tendency of the IQ scores in the sample.
Step-by-step explanation:
The question asks for the calculation of various statistical measures for a data set of IQ scores, assuming a normal distribution. To answer this question, some of the key concepts – such as mean, median, mode, range, interquartile range, variance, and standard deviation – must be computed using the set of IQ scores provided, through either manual calculations or statistical software such as Excel or SPSS.
The mean is the average score, median is the middle value when the scores are ordered, mode is the most frequent score, range is the difference between the highest and lowest scores, interquartile range (IQR) measures the middle 50% of data, variance is the average of the squared deviations from the mean, and standard deviation is the square root of variance, indicating how much the scores deviate from the mean, on average.
Steps to Calculate the Statistics:
- Order the data set from smallest to largest.
- Determine the mode by identifying the most frequent score(s).
- Calculate the mean by adding all scores together and dividing by the number of scores.
- Find the median by locating the middle score in the ordered data set, which for an even number of data points is the average of the two middle numbers.
- Compute the range by subtracting the smallest score from the largest score.
- To get the IQR, find the first quartile (Q1, 25th percentile) and the third quartile (Q3, 75th percentile) and then subtract Q1 from Q3.
- Calculate variance using the formula for the sum of squared differences from the mean, divided by the number of scores minus one.
- Finally, take the square root of variance to get the standard deviation.
These measures are essential for understanding the distribution of IQ scores among the students in the sample.