Apply suggestions from code review

Co-authored-by: Phillip Carter <pcarter@fastmail.com>

content/en/blog/2023/why-histograms/index.md

@@ -7,23 +7,21 @@ author: '[Daniel Dyla](https://github.com/dyladan)'
 <i>Originally posted to
 https://dyladan.me/histograms/2023/05/02/why-histograms/</i>
 
-A histogram is a multi-value counter which summarizes the distribution of one or
-more data points. For example, a histogram may have 3 counters which count the
+A histogram is a multi-value counter that summarizes the distribution of data points.
+For example, a histogram may have 3 counters which count the
 occurrences of negative, positive, and zero values respectively. Given a series
 of numbers, `3`, `-9`, `7`, `6`, `0`, and `-1`, the histogram would count `2`
 negative, `1` zero, and `3` positive values. A single histogram data point is
 most commonly represented as a bar chart.
 
 ![histogram point as bar chart](hist-point.png "A single histogram point plotted as a bar chart with 3 buckets titled 'Positivity of numbers'. The first bucket shows negative numbers and has a height of 2. The second bucket shows zero values and has a height of 1. The third bucket shows positive values and has a height of 3.")
 
-This simple example has only 3 possible output values, but it is not uncommon to
-have many more in a single histogram. Similarly, this shows only 1 histogram
-data point, but in the world of observability data is usually constantly
-exported. For example, an application may export a histogram every minute which
-summarizes a metric for the previous minute. In this way, you can study how the
-distribution of your data changes over time.
+The above example has only 3 possible output values, but it is common to
+have many more in a single histogram. A real-world application typically exports
+a histogram every minute that summarizes a metric for the previous minute.
+By using histograms this way, you can study how the distribution of your data changes over time.
 
-# What are histograms for?
+## What are histograms for?
 
 There are many uses for histograms, but their power comes from the ability to
 efficiently answer queries about the distribution of your data. These queries
@@ -33,7 +31,7 @@ shorthand like `p50` for the 50th percentile or 0.5-quantile, also known as the
 median. More generally, the φ-quantile is the observation value that ranks at
 number φ\*N among the N observations.
 
-# Why is that useful?
+## Why are Histograms useful?
 
 The most common use-case for histograms in the observability space is defining
 service level objectives (SLOs). One example of such an SLO might be ">=99% of
@@ -50,7 +48,7 @@ under 90ms.
 
 ![p99, p90, and p50 plotted as lines](hist-lines.png "p99, p90, and p50 plotted as a line chart with title 'response times.' Time is on the x-axis and response times in milliseconds on the y-axis. p99 response times are around 80 milliseconds. p90 response times are betweeen 60 and 80 milliseconds. p50 response times are between 20 and 30 milliseconds.")
 
-# Other metric types
+## Other metric types
 
 Another solution might be to define the SLOs you're interested in and collect
 them as non-histogram metrics in advance as gauges or counters. This approach
@@ -65,16 +63,16 @@ already collected. Particularly with exponential histograms, arbitrary
 distribution queries can be made with very low relative error rates and minimal
 resource consumption on both the client and the analysis backend.
 
-The inflexibility of this approach also impacts your ability to gauge impact
-when your SLO is violated. For example, imagine you are collecting a gauge which
+The inflexibility of not using histograms for SLOs also impacts your ability to gauge impact
+when your SLO is violated. For example, imagine you are collecting a gauge that
 calculates the `p99` of some metric and you define an SLO based on it. When your
 SLO is violated and an alert is triggered, how do you know it is really only
-affecting 1% of queries, 10%, or 50%? A histogram would allow you to answer that
-question by simply querying the percentiles you're interested in. You could
-collect additional gauges for each percentile, but then you've just force users
-to reimplement histograms on their own. Probably poorly.
+affecting 1% of queries, 10%, or 50%? A histogram allows you to answer that
+question by querying the percentiles you're interested in. You could technically
+collect additional gauges for each percentile, but that's just an ad-hoc reimplementation
+of histograms anyways, so you're better off using histograms.
 
-# Other data sources and metric types
+## Other data sources and metric types
 
 You may ask why you would report a separate metric rather than calculating these
 metrics from your existing log and trace data? While it is true that for _some_