Analyzing Histograms Using Shape and Spread

A left-skewed distribution has a longer tail on the left, indicating more values on the right. In a histogram, this shows a peak on the right side with fewer low values, leading to the conclusion that the distribution is left-skewed.

The range is the difference between the maximum (14 hours) and minimum (2 hours) study times. Calculate: 14 - 2 = 12. The average study time (10 hours) provides a central value, making B the best choice.

The peak of the distribution occurs in the interval where most data points cluster. Here, the highest frequency of data is observed in the 6–8 hours range, making it the mode.

The center of data distribution is often indicated by the range. Here, 6–7 hours suggests a central tendency around these values, showing that the majority of data lies within this interval.

The histogram shows a concentration of ages on the left and a tail extending to the right. This indicates that the majority of data falls at the lower end, making it right-skewed.

In a uniform distribution, each bar in the histogram represents an equal frequency of data values, resulting in approximately the same height across all bars. This indicates even spread without concentration in any area.

A symmetric distribution has equal tails on both sides. The mean, median, and mode are all equal, showing balance. This symmetry indicates no skewness, confirming option A as the correct shape.

The nearly equal height of bars indicates that all score intervals have a similar frequency, suggesting that the data is uniformly distributed. This means every score range has about the same number of occurrences, which confirms option D as the correct choice.

The average daily step goal is often set at 10,000 steps, but many health guidelines suggest a healthy range can go up to 12,000 steps for active individuals, making 12,000 a more realistic benchmark.

In a symmetric histogram, the data is evenly distributed around the center, leading to the mean and median being approximately equal. This balance indicates no skewness, making option A the correct choice.

To determine the interval with the most users, compare the user counts: 6–8 thousand contains the most users based on survey data analysis. Simply check the frequency distribution to see that this range has the highest count.

The histogram shows varied heights across intervals, indicating a moderate spread of data. A tightly clustered data would show less variation, while extreme outliers would appear as isolated bars. Option C reflects this moderate distribution.

The left tail indicates a left-skewed distribution. Most values cluster on the right, causing the left tail to extend. This imbalance confirms that the distribution is left-skewed.

The spread of a histogram indicates the variability of the data. A wider spread means greater variation in values, while a narrower spread indicates less variation.

A symmetric distribution, like a bell curve, has equal values on both sides of the center, indicating that most students have heights close to the average.

A right-skewed distribution indicates that most commute times are shorter, with a few long commutes pulling the average higher. Analyzing Company A's data shows this pattern clearly.

The answer is 'Both have the same range' because it indicates that neither company has a greater or lesser range of commute times when compared to the other. Therefore, their ranges are equal.

To determine the concentration of commute times, compare the frequency of lower intervals. If Company A has a higher percentage of employees with shorter commute times, it shows more concentration in lower intervals, confirming the answer is C.

A right-skewed distribution has a longer tail on the right, indicating fewer high values. In the histogram, as the bars decrease from left to right, it shows that most students read fewer books, validating option A as the correct answer.

The spread or range of the data indicates variability by showing how much the values differ from each other. A wider range means greater variability, highlighting more diverse data points in the histogram.